Discrete Applied Mathematics最新文献
筛选
英文
中文
Reliability analysis of godan graphs in terms of generalized 4-connectivity
IF 1
3区 数学
Jing Wang , Zhangdong Ouyang , Yuanqiu Huang
{"title":"Reliability analysis of godan graphs in terms of generalized 4-connectivity","authors":"Jing Wang , Zhangdong Ouyang , Yuanqiu Huang","doi":"10.1016/j.dam.2025.04.026","DOIUrl":"10.1016/j.dam.2025.04.026","url":null,"abstract":"<div><div>Let <span><math><mi>G</mi></math></span> be a connected graph and <span><math><mrow><mi>S</mi><mo>⊆</mo><mi>V</mi><mrow><mo>(</mo><mi>G</mi><mo>)</mo></mrow></mrow></math></span>. Denote by <span><math><mrow><msub><mrow><mi>κ</mi></mrow><mrow><mi>G</mi></mrow></msub><mrow><mo>(</mo><mi>S</mi><mo>)</mo></mrow></mrow></math></span> the maximum number <span><math><mi>r</mi></math></span> of internally disjoint <span><math><mi>S</mi></math></span>-trees <span><math><msub><mrow><mi>T</mi></mrow><mrow><mn>1</mn></mrow></msub></math></span>, <span><math><msub><mrow><mi>T</mi></mrow><mrow><mn>2</mn></mrow></msub></math></span>, <span><math><mo>…</mo></math></span>, <span><math><msub><mrow><mi>T</mi></mrow><mrow><mi>r</mi></mrow></msub></math></span> in <span><math><mi>G</mi></math></span> such that <span><math><mrow><mi>V</mi><mrow><mo>(</mo><msub><mrow><mi>T</mi></mrow><mrow><mi>i</mi></mrow></msub><mo>)</mo></mrow><mo>∩</mo><mi>V</mi><mrow><mo>(</mo><msub><mrow><mi>T</mi></mrow><mrow><mi>j</mi></mrow></msub><mo>)</mo></mrow><mo>=</mo><mi>S</mi></mrow></math></span> and <span><math><mrow><mi>E</mi><mrow><mo>(</mo><msub><mrow><mi>T</mi></mrow><mrow><mi>i</mi></mrow></msub><mo>)</mo></mrow><mo>∩</mo><mi>E</mi><mrow><mo>(</mo><msub><mrow><mi>T</mi></mrow><mrow><mi>j</mi></mrow></msub><mo>)</mo></mrow><mo>=</mo><mo>0̸</mo></mrow></math></span> for any integers <span><math><mrow><mn>1</mn><mo>≤</mo><mi>i</mi><mo><</mo><mi>j</mi><mo>≤</mo><mi>r</mi></mrow></math></span>. For an integer <span><math><mi>k</mi></math></span> with <span><math><mrow><mn>2</mn><mo>≤</mo><mi>k</mi><mo>≤</mo><mrow><mo>|</mo><mi>V</mi><mrow><mo>(</mo><mi>G</mi><mo>)</mo></mrow><mo>|</mo></mrow></mrow></math></span>, the generalized <span><math><mi>k</mi></math></span>-connectivity of a graph <span><math><mi>G</mi></math></span>, denoted by <span><math><mrow><msub><mrow><mi>κ</mi></mrow><mrow><mi>k</mi></mrow></msub><mrow><mo>(</mo><mi>G</mi><mo>)</mo></mrow></mrow></math></span>, is defined as <span><math><mrow><msub><mrow><mi>κ</mi></mrow><mrow><mi>k</mi></mrow></msub><mrow><mo>(</mo><mi>G</mi><mo>)</mo></mrow><mo>=</mo><mo>min</mo><mtext>{</mtext><msub><mrow><mi>κ</mi></mrow><mrow><mi>G</mi></mrow></msub><mrow><mo>(</mo><mi>S</mi><mo>)</mo></mrow><mo>|</mo><mi>S</mi><mo>⊆</mo><mi>V</mi><mrow><mo>(</mo><mi>G</mi><mo>)</mo></mrow></mrow></math></span> and <span><math><mrow><mrow><mo>|</mo><mi>S</mi><mo>|</mo></mrow><mo>=</mo><mi>k</mi><mtext>}</mtext></mrow></math></span>. The generalized <span><math><mi>k</mi></math></span>-connectivity of a graph is a natural extension of the classical connectivity and plays a key role in measuring the reliability of modern interconnection networks. The godan graph <span><math><mrow><mi>E</mi><msub><mrow><mi>A</mi></mrow><mrow><mi>n</mi></mrow></msub></mrow></math></span> is a kind of Cayley graph which possess many desirable properties. In this paper, we study the generalized 4-connectivity of <span><math><mrow><mi>E</mi><msub><mrow><m","PeriodicalId":50573,"journal":{"name":"Discrete Applied Mathematics","volume":"372 ","pages":"Pages 210-223"},"PeriodicalIF":1.0,"publicationDate":"2025-04-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143859936","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Two problems on Laplacian ratios of trees
IF 1
3区 数学
Tingzeng Wu , Xiangshuai Dong , Hong-Jian Lai
{"title":"Two problems on Laplacian ratios of trees","authors":"Tingzeng Wu , Xiangshuai Dong , Hong-Jian Lai","doi":"10.1016/j.dam.2025.04.047","DOIUrl":"10.1016/j.dam.2025.04.047","url":null,"abstract":"<div><div>The Laplacian ratio of graph <span><math><mi>G</mi></math></span> is the permanent of the Laplacian matrix of <span><math><mi>G</mi></math></span> divided by the product of degrees of all vertices. Brualdi and Goldwasser investigated systematically bounds of Laplacian ratios of trees. And they proposed two open problems: one is to characterize the extremal value of the Laplacian ratios of trees with given bipartition, the other is to determine the maximum value of the Laplacian ratios of trees. In this article, we give a solution of the first problem. We determine the lower bound of Laplacian ratios of trees with given bipartition, and the corresponding extremal graph is also determined. On the second problem, we give a conjecture on the upper bound of Laplacian ratios of trees. Furthermore, we also determine Laplacian ratios of some special trees that support the conjecture.</div></div>","PeriodicalId":50573,"journal":{"name":"Discrete Applied Mathematics","volume":"372 ","pages":"Pages 224-236"},"PeriodicalIF":1.0,"publicationDate":"2025-04-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143864657","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Some results on the saturation number of graphs
IF 1
3区 数学
Jinze Hu , Shengjin Ji , Chenke Zhang
{"title":"Some results on the saturation number of graphs","authors":"Jinze Hu , Shengjin Ji , Chenke Zhang","doi":"10.1016/j.dam.2025.04.038","DOIUrl":"10.1016/j.dam.2025.04.038","url":null,"abstract":"<div><div>For a given graph <span><math><mi>F</mi></math></span>, we say a (connected) graph <span><math><mi>G</mi></math></span> is (connected) <span><math><mi>F</mi></math></span>-saturated if <span><math><mi>G</mi></math></span> is <span><math><mi>F</mi></math></span>-free, and for any <span><math><mrow><mi>e</mi><mo>∈</mo><mi>E</mi><mrow><mo>(</mo><mover><mrow><mi>G</mi></mrow><mo>¯</mo></mover><mo>)</mo></mrow></mrow></math></span>, <span><math><mrow><mi>G</mi><mo>+</mo><mi>e</mi></mrow></math></span> creates an <span><math><mi>F</mi></math></span>-copy. The (connected) saturation number is the minimum number of edges of a (connected) <span><math><mi>F</mi></math></span>-saturated graph with <span><math><mi>n</mi></math></span> vertices. We denote the saturation number and the connected saturation number by <span><math><mrow><mi>s</mi><mi>a</mi><mi>t</mi><mrow><mo>(</mo><mi>n</mi><mo>,</mo><mi>F</mi><mo>)</mo></mrow></mrow></math></span> and <span><math><mrow><mi>s</mi><mi>a</mi><msub><mrow><mi>t</mi></mrow><mrow><mi>c</mi></mrow></msub><mrow><mo>(</mo><mi>n</mi><mo>,</mo><mi>F</mi><mo>)</mo></mrow></mrow></math></span>, respectively. Evidently, <span><math><mrow><mi>s</mi><mi>a</mi><mi>t</mi><mrow><mo>(</mo><mi>n</mi><mo>,</mo><mi>F</mi><mo>)</mo></mrow><mo>≤</mo><mi>s</mi><mi>a</mi><msub><mrow><mi>t</mi></mrow><mrow><mi>c</mi></mrow></msub><mrow><mo>(</mo><mi>n</mi><mo>,</mo><mi>F</mi><mo>)</mo></mrow></mrow></math></span>. A generalized friendship graph is regarded as the join of a clique and the union of some disjoint cliques. In this paper, we show the relationship of the saturation numbers between the unions of disjoint cliques and generalized friendship graphs, and as its application, obtain the saturation numbers of some generalized friendship graphs. And then we propose respectively two sufficient conditions for <span><math><mrow><mi>s</mi><mi>a</mi><mi>t</mi><mrow><mo>(</mo><mi>n</mi><mo>,</mo><mi>F</mi><mo>)</mo></mrow><mo>=</mo><mi>s</mi><mi>a</mi><msub><mrow><mi>t</mi></mrow><mrow><mi>c</mi></mrow></msub><mrow><mo>(</mo><mi>n</mi><mo>,</mo><mi>F</mi><mo>)</mo></mrow></mrow></math></span> and <span><math><mrow><mi>s</mi><mi>a</mi><mi>t</mi><mrow><mo>(</mo><mi>n</mi><mo>,</mo><mi>F</mi><mo>)</mo></mrow><mo><</mo><mi>s</mi><mi>a</mi><msub><mrow><mi>t</mi></mrow><mrow><mi>c</mi></mrow></msub><mrow><mo>(</mo><mi>n</mi><mo>,</mo><mi>F</mi><mo>)</mo></mrow></mrow></math></span>. In addition, we show <span><math><mrow><mi>s</mi><mi>a</mi><msub><mrow><mi>t</mi></mrow><mrow><mi>c</mi></mrow></msub><mrow><mo>(</mo><mi>n</mi><mo>,</mo><msub><mrow><mi>P</mi></mrow><mrow><mi>k</mi></mrow></msub><mo>∪</mo><msub><mrow><mi>K</mi></mrow><mrow><mn>3</mn></mrow></msub><mo>)</mo></mrow><mo>=</mo><mi>n</mi><mo>+</mo><mn>2</mn></mrow></math></span> for sufficiently large <span><math><mi>n</mi></math></span> and <span><math><mrow><mi>k</mi><mo>≥</mo><mn>4</mn></mrow></math></span>. Furthermore, we obtain an upper bound of the saturation number of <s","PeriodicalId":50573,"journal":{"name":"Discrete Applied Mathematics","volume":"372 ","pages":"Pages 188-196"},"PeriodicalIF":1.0,"publicationDate":"2025-04-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143864656","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Spectral conditions for component factors in graphs involving minimum degree
IF 1
3区 数学
Zhiren Sun , Sizhong Zhou
{"title":"Spectral conditions for component factors in graphs involving minimum degree","authors":"Zhiren Sun , Sizhong Zhou","doi":"10.1016/j.dam.2025.04.017","DOIUrl":"10.1016/j.dam.2025.04.017","url":null,"abstract":"<div><div>A spanning subgraph <span><math><mi>H</mi></math></span> of a graph <span><math><mi>G</mi></math></span> is called an <span><math><mrow><mo>{</mo><msub><mrow><mi>P</mi></mrow><mrow><mn>2</mn></mrow></msub><mo>,</mo><msub><mrow><mi>C</mi></mrow><mrow><mn>3</mn></mrow></msub><mo>,</mo><msub><mrow><mi>P</mi></mrow><mrow><mn>5</mn></mrow></msub><mo>,</mo><mi>T</mi><mrow><mo>(</mo><mn>3</mn><mo>)</mo></mrow><mo>}</mo></mrow></math></span>-factor if every component of <span><math><mi>H</mi></math></span> is isomorphic to an element of <span><math><mrow><mo>{</mo><msub><mrow><mi>P</mi></mrow><mrow><mn>2</mn></mrow></msub><mo>,</mo><msub><mrow><mi>C</mi></mrow><mrow><mn>3</mn></mrow></msub><mo>,</mo><msub><mrow><mi>P</mi></mrow><mrow><mn>5</mn></mrow></msub><mo>,</mo><mi>T</mi><mrow><mo>(</mo><mn>3</mn><mo>)</mo></mrow><mo>}</mo></mrow></math></span>, where <span><math><mrow><mi>T</mi><mrow><mo>(</mo><mn>3</mn><mo>)</mo></mrow></mrow></math></span> is one special family of tree. Let <span><math><mrow><mi>A</mi><mrow><mo>(</mo><mi>G</mi><mo>)</mo></mrow></mrow></math></span> and <span><math><mrow><mi>Q</mi><mrow><mo>(</mo><mi>G</mi><mo>)</mo></mrow></mrow></math></span> denote the adjacency matrix and the signless Laplacian matrix of <span><math><mi>G</mi></math></span>, respectively. The largest eigenvalues of <span><math><mrow><mi>A</mi><mrow><mo>(</mo><mi>G</mi><mo>)</mo></mrow></mrow></math></span> and <span><math><mrow><mi>Q</mi><mrow><mo>(</mo><mi>G</mi><mo>)</mo></mrow></mrow></math></span>, denoted by <span><math><mrow><mi>ρ</mi><mrow><mo>(</mo><mi>G</mi><mo>)</mo></mrow></mrow></math></span> and <span><math><mrow><mi>q</mi><mrow><mo>(</mo><mi>G</mi><mo>)</mo></mrow></mrow></math></span>, are called the adjacency spectral radius and the signless Laplacian spectral radius of <span><math><mi>G</mi></math></span>, respectively. In this paper, we first present a sufficient condition to guarantee that a connected graph <span><math><mi>G</mi></math></span> with minimum degree <span><math><mi>δ</mi></math></span> contains a <span><math><mrow><mo>{</mo><msub><mrow><mi>P</mi></mrow><mrow><mn>2</mn></mrow></msub><mo>,</mo><msub><mrow><mi>C</mi></mrow><mrow><mn>3</mn></mrow></msub><mo>,</mo><msub><mrow><mi>P</mi></mrow><mrow><mn>5</mn></mrow></msub><mo>,</mo><mi>T</mi><mrow><mo>(</mo><mn>3</mn><mo>)</mo></mrow><mo>}</mo></mrow></math></span>-factor with respect to its adjacency spectral radius, then we claim a sufficient condition to ensure that a connected graph <span><math><mi>G</mi></math></span> with minimum degree <span><math><mi>δ</mi></math></span> has a <span><math><mrow><mo>{</mo><msub><mrow><mi>P</mi></mrow><mrow><mn>2</mn></mrow></msub><mo>,</mo><msub><mrow><mi>C</mi></mrow><mrow><mn>3</mn></mrow></msub><mo>,</mo><msub><mrow><mi>P</mi></mrow><mrow><mn>5</mn></mrow></msub><mo>,</mo><mi>T</mi><mrow><mo>(</mo><mn>3</mn><mo>)</mo></mrow><mo>}</mo></mrow></math></span>-factor via its signless Laplacian spectral radius.</div></div>","PeriodicalId":50573,"journal":{"name":"Discrete Applied Mathematics","volume":"372 ","pages":"Pages 180-187"},"PeriodicalIF":1.0,"publicationDate":"2025-04-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143856036","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Perfect matchings of (4,6)-fullerenes with largest forcing number
IF 1
3区 数学
Yaxian Zhang, Heping Zhang
{"title":"Perfect matchings of (4,6)-fullerenes with largest forcing number","authors":"Yaxian Zhang, Heping Zhang","doi":"10.1016/j.dam.2025.04.004","DOIUrl":"10.1016/j.dam.2025.04.004","url":null,"abstract":"<div><div>Clar number (or resonant number) is a thoroughly investigated parameter of plane graphs emerging from mathematical chemistry to measure stability of some organic molecules. It was shown that the Clar number of a <span><math><mrow><mo>(</mo><mn>4</mn><mo>,</mo><mn>6</mn><mo>)</mo></mrow></math></span>-fullerene graph <span><math><mi>G</mi></math></span>, a plane cubic graph with only hexagonal and quadrilateral faces, is equal to its maximum forcing number <span><math><mrow><mi>F</mi><mrow><mo>(</mo><mi>G</mi><mo>)</mo></mrow></mrow></math></span>. Let <span><math><mi>M</mi></math></span> be any perfect matching of <span><math><mi>G</mi></math></span> attaining the maximum forcing number. We use <span><math><mrow><mi>C</mi><mrow><mo>(</mo><mi>G</mi><mo>,</mo><mi>M</mi><mo>)</mo></mrow></mrow></math></span> and <span><math><mrow><mi>C</mi><mrow><mo>(</mo><mi>G</mi><mo>,</mo><mi>M</mi><mo>)</mo></mrow></mrow></math></span> to denote two largest sets of disjoint <span><math><mi>M</mi></math></span>-alternating cycles and <span><math><mi>M</mi></math></span>-alternating facial cycles respectively. Then <span><math><mrow><mi>F</mi><mrow><mo>(</mo><mi>G</mi><mo>)</mo></mrow><mo>=</mo><mrow><mo>|</mo><mi>C</mi><mrow><mo>(</mo><mi>G</mi><mo>,</mo><mi>M</mi><mo>)</mo></mrow><mo>|</mo></mrow><mo>≥</mo><mrow><mo>|</mo><mi>C</mi><mrow><mo>(</mo><mi>G</mi><mo>,</mo><mi>M</mi><mo>)</mo></mrow><mo>|</mo></mrow></mrow></math></span>. In this paper, we consider when <span><math><mrow><mrow><mo>|</mo><mi>C</mi><mrow><mo>(</mo><mi>G</mi><mo>,</mo><mi>M</mi><mo>)</mo></mrow><mo>|</mo></mrow><mo>=</mo><mrow><mo>|</mo><mi>C</mi><mrow><mo>(</mo><mi>G</mi><mo>,</mo><mi>M</mi><mo>)</mo></mrow><mo>|</mo></mrow></mrow></math></span> holds. First we show that every cycle in <span><math><mrow><mi>C</mi><mrow><mo>(</mo><mi>G</mi><mo>,</mo><mi>M</mi><mo>)</mo></mrow></mrow></math></span> has length 4, 6, 8 or 12. Then we construct two types of tubular <span><math><mrow><mo>(</mo><mn>4</mn><mo>,</mo><mn>6</mn><mo>)</mo></mrow></math></span>-fullerene graphs <span><math><msub><mrow><mi>G</mi></mrow><mrow><mn>1</mn></mrow></msub></math></span> and <span><math><msub><mrow><mi>G</mi></mrow><mrow><mn>2</mn></mrow></msub></math></span> so that there is a <span><math><mrow><mi>C</mi><mrow><mo>(</mo><mi>G</mi><mo>,</mo><mi>M</mi><mo>)</mo></mrow></mrow></math></span> containing a 12-cycle if and only if <span><math><mrow><mi>G</mi><mo>∈</mo><msub><mrow><mi>G</mi></mrow><mrow><mn>1</mn></mrow></msub></mrow></math></span>, and there is a <span><math><mrow><mi>C</mi><mrow><mo>(</mo><mi>G</mi><mo>,</mo><mi>M</mi><mo>)</mo></mrow></mrow></math></span> containing a 8-cycle if and only if <span><math><mrow><mi>G</mi><mo>∈</mo><msub><mrow><mi>G</mi></mrow><mrow><mn>2</mn></mrow></msub></mrow></math></span>. As a consequence, we obtain the following three equivalent statements: (i) Each <span><math><mrow><mi>C</mi><mrow><mo>(</mo><mi>G</mi><mo>,</mo><mi>M</mi><mo>)</mo></mrow></mrow></","PeriodicalId":50573,"journal":{"name":"Discrete Applied Mathematics","volume":"373 ","pages":"Pages 10-25"},"PeriodicalIF":1.0,"publicationDate":"2025-04-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143851791","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Ore-type condition for Hamilton ℓ-cycle in k-uniform hypergraphs
IF 1
3区 数学
Taijiang Jiang , Qiang Sun , Chao Zhang
{"title":"Ore-type condition for Hamilton ℓ-cycle in k-uniform hypergraphs","authors":"Taijiang Jiang , Qiang Sun , Chao Zhang","doi":"10.1016/j.dam.2025.04.036","DOIUrl":"10.1016/j.dam.2025.04.036","url":null,"abstract":"<div><div>The classic Ore theorem states that if the degree sum of any two non-adjacent vertices in an <span><math><mi>n</mi></math></span>-vertex graph is at least <span><math><mi>n</mi></math></span>, then the graph contains a Hamilton cycle. Tang and Yan extended this result to hypergraphs in 2017 and obtained an Ore-type condition for the existence of tight Hamilton cycles. In this paper, we consider the Ore-type sufficient condition for the existence of Hamilton <span><math><mi>ℓ</mi></math></span>-cycles. Our main result is that for <span><math><mrow><mi>k</mi><mo>≥</mo><mn>3</mn></mrow></math></span>, <span><math><mrow><mn>1</mn><mo>≤</mo><mi>ℓ</mi><mo><</mo><mi>k</mi><mo>/</mo><mn>2</mn></mrow></math></span>, <span><math><mrow><mi>γ</mi><mo>></mo><mn>0</mn></mrow></math></span> and for sufficiently large <span><math><mi>n</mi></math></span> with <span><math><mrow><mi>n</mi><mo>∈</mo><mrow><mo>(</mo><mi>k</mi><mo>−</mo><mi>ℓ</mi><mo>)</mo></mrow><mi>N</mi></mrow></math></span>, every <span><math><mi>k</mi></math></span>-uniform hypergraph <span><math><mrow><mi>H</mi><mo>=</mo><mrow><mo>(</mo><mi>V</mi><mo>,</mo><mi>E</mi><mo>)</mo></mrow></mrow></math></span> on <span><math><mi>n</mi></math></span> vertices with the degree sum of any two weakly independent sets at least <span><math><mrow><mrow><mo>(</mo><mfrac><mrow><mn>3</mn></mrow><mrow><mn>2</mn><mrow><mo>(</mo><mi>k</mi><mo>−</mo><mi>ℓ</mi><mo>)</mo></mrow></mrow></mfrac><mo>+</mo><mi>γ</mi><mo>)</mo></mrow><mi>n</mi></mrow></math></span> contains a Hamilton <span><math><mi>ℓ</mi></math></span>-cycle.</div></div>","PeriodicalId":50573,"journal":{"name":"Discrete Applied Mathematics","volume":"371 ","pages":"Pages 270-275"},"PeriodicalIF":1.0,"publicationDate":"2025-04-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143855998","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Unit dual quaternion directed graphs, formation control and general weighted directed graphs
IF 1
3区 数学
Liqun Qi , Chunfeng Cui , Chen Ouyang
{"title":"Unit dual quaternion directed graphs, formation control and general weighted directed graphs","authors":"Liqun Qi , Chunfeng Cui , Chen Ouyang","doi":"10.1016/j.dam.2025.04.027","DOIUrl":"10.1016/j.dam.2025.04.027","url":null,"abstract":"<div><div>We study the multi-agent formation control problem in a directed graph. The relative configurations are expressed by unit dual quaternions (UDQs). We call such a weighted directed graph a unit dual quaternion directed graph (UDQDG). We show that a desired relative configuration scheme is reasonable or balanced in a UDQDG if and only if there is a diagonal matrix with UDQ diagonal elements such that the dual quaternion Laplacian is similar to the unweighted Laplacian of the underlying directed graph. A direct method and a unit gain graph method are proposed to solve the balance problem of general unit weighted directed graphs. We then study the balance problem of general non-unit weighted directed graphs. Numerical experiments for UDQDG are reported.</div></div>","PeriodicalId":50573,"journal":{"name":"Discrete Applied Mathematics","volume":"372 ","pages":"Pages 197-209"},"PeriodicalIF":1.0,"publicationDate":"2025-04-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143856013","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Matching polynomials of path-trees of a complete bipartite graph
完整双向图路径树的匹配多项式
IF 1
3区 数学
Haiyan Chen , Yinxia Yuan
{"title":"Matching polynomials of path-trees of a complete bipartite graph","authors":"Haiyan Chen , Yinxia Yuan","doi":"10.1016/j.dam.2025.04.014","DOIUrl":"10.1016/j.dam.2025.04.014","url":null,"abstract":"<div><div>Suppose that the vertex set of the complete bipartite graph <span><math><msub><mrow><mi>K</mi></mrow><mrow><mi>s</mi><mo>,</mo><mi>t</mi></mrow></msub></math></span> is <span><math><mrow><mi>X</mi><mo>∪</mo><mi>Y</mi></mrow></math></span>, where <span><math><mrow><mo>|</mo><mi>X</mi><mo>|</mo><mo>=</mo><mi>s</mi><mo>≤</mo><mi>t</mi><mo>=</mo><mo>|</mo><mi>Y</mi><mo>|</mo></mrow></math></span>. Let <span><math><msubsup><mrow><mi>T</mi></mrow><mrow><mi>s</mi><mo>,</mo><mi>t</mi></mrow><mrow><mi>w</mi></mrow></msubsup></math></span> denote the path-tree of <span><math><msub><mrow><mi>K</mi></mrow><mrow><mi>s</mi><mo>,</mo><mi>t</mi></mrow></msub></math></span> corresponding to vertex <span><math><mrow><mi>w</mi><mo>∈</mo><mi>X</mi><mo>∪</mo><mi>Y</mi></mrow></math></span>. Then we show that the matching polynomial <span><math><mrow><mi>μ</mi><mrow><mo>(</mo><msubsup><mrow><mi>T</mi></mrow><mrow><mi>s</mi><mo>,</mo><mi>t</mi></mrow><mrow><mi>w</mi></mrow></msubsup><mo>,</mo><mi>x</mi><mo>)</mo></mrow></mrow></math></span> is equal to <span><math><mrow><mi>μ</mi><mrow><mo>(</mo><msub><mrow><mi>K</mi></mrow><mrow><mi>s</mi><mo>,</mo><mi>t</mi></mrow></msub><mo>,</mo><mi>x</mi><mo>)</mo></mrow><mi>⋅</mi></mrow></math></span>\u0000 <span><math><mfenced><mrow><mtable><mtr><mtd><msup><mrow><mfenced><mrow><munderover><mrow><mo>∏</mo></mrow><mrow><mi>k</mi><mo>=</mo><mn>1</mn></mrow><mrow><mi>s</mi><mo>−</mo><mn>1</mn></mrow></munderover><msup><mrow><mfenced><mrow><mi>μ</mi><msup><mrow><mrow><mo>(</mo><msub><mrow><mi>K</mi></mrow><mrow><mi>k</mi><mo>,</mo><mi>α</mi><mo>+</mo><mi>k</mi></mrow></msub><mo>,</mo><mi>x</mi><mo>)</mo></mrow></mrow><mrow><mi>k</mi><mo>−</mo><mn>1</mn></mrow></msup><mi>μ</mi><msup><mrow><mrow><mo>(</mo><msub><mrow><mi>K</mi></mrow><mrow><mi>k</mi><mo>,</mo><mi>α</mi><mo>+</mo><mi>k</mi><mo>+</mo><mn>1</mn></mrow></msub><mo>,</mo><mi>x</mi><mo>)</mo></mrow></mrow><mrow><mfrac><mrow><mi>α</mi><mo>+</mo><mi>k</mi></mrow><mrow><mi>α</mi><mo>+</mo><mi>k</mi><mo>+</mo><mn>1</mn></mrow></mfrac></mrow></msup></mrow></mfenced></mrow><mrow><msubsup><mrow><mi>β</mi></mrow><mrow><mi>s</mi><mo>,</mo><mi>t</mi></mrow><mrow><mi>k</mi></mrow></msubsup></mrow></msup></mrow></mfenced></mrow><mrow><mi>t</mi></mrow></msup><mo>,</mo></mtd><mtd><mspace></mspace><mtext> if </mtext><mi>w</mi><mo>∈</mo><mi>X</mi><mo>;</mo></mtd></mtr><mtr><mtd><mi>μ</mi><msup><mrow><mrow><mo>(</mo><msub><mrow><mi>K</mi></mrow><mrow><mi>s</mi><mo>,</mo><mi>t</mi><mo>−</mo><mn>1</mn></mrow></msub><mo>,</mo><mi>x</mi><mo>)</mo></mrow></mrow><mrow><mi>s</mi><mo>−</mo><mn>1</mn></mrow></msup><msup><mrow><mfenced><mrow><munderover><mrow><mo>∏</mo></mrow><mrow><mi>k</mi><mo>=</mo><mn>1</mn></mrow><mrow><mi>s</mi><mo>−</mo><mn>1</mn></mrow></munderover><msup><mrow><mfenced><mrow><mi>μ</mi><msup><mrow><mrow><mo>(</mo><msub><mrow><mi>K</mi></mrow><mrow><mi>k</mi><mo>,</mo><mi>α</mi><mo>+</mo><mi>k</mi><mo>−</mo><mn>1</mn></mrow></msub><mo>,</mo><mi>x</mi><mo>)</mo></mrow></mrow>","PeriodicalId":50573,"journal":{"name":"Discrete Applied Mathematics","volume":"372 ","pages":"Pages 173-179"},"PeriodicalIF":1.0,"publicationDate":"2025-04-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143851864","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
An (F3,F4)-partition of planar graphs without 4- and 6-cycles
IF 1
3区 数学
Kaiyang Hu, Mingfang Huang
{"title":"An (F3,F4)-partition of planar graphs without 4- and 6-cycles","authors":"Kaiyang Hu, Mingfang Huang","doi":"10.1016/j.dam.2025.04.018","DOIUrl":"10.1016/j.dam.2025.04.018","url":null,"abstract":"<div><div>An <span><math><mrow><mo>(</mo><msub><mrow><mi>F</mi></mrow><mrow><msub><mrow><mi>d</mi></mrow><mrow><mn>1</mn></mrow></msub></mrow></msub><mo>,</mo><mo>…</mo><mo>,</mo><msub><mrow><mi>F</mi></mrow><mrow><msub><mrow><mi>d</mi></mrow><mrow><mi>k</mi></mrow></msub></mrow></msub><mo>)</mo></mrow></math></span>-partition of a graph <span><math><mi>G</mi></math></span> is a partition of its vertices set into <span><math><mi>k</mi></math></span> subsets <span><math><mrow><msub><mrow><mi>V</mi></mrow><mrow><mn>1</mn></mrow></msub><mo>,</mo><mo>…</mo><mo>,</mo><msub><mrow><mi>V</mi></mrow><mrow><mi>k</mi></mrow></msub></mrow></math></span> where each <span><math><msub><mrow><mi>V</mi></mrow><mrow><mi>i</mi></mrow></msub></math></span> induces a forest with maximum degree at most <span><math><msub><mrow><mi>d</mi></mrow><mrow><mi>i</mi></mrow></msub></math></span> for <span><math><mrow><mi>i</mi><mo>∈</mo><mrow><mo>{</mo><mn>1</mn><mo>,</mo><mo>…</mo><mo>,</mo><mi>k</mi><mo>}</mo></mrow></mrow></math></span>. Cho et al.(2021) proved that every planar graph without 4- and 5-cycles admits an <span><math><mrow><mo>(</mo><msub><mrow><mi>F</mi></mrow><mrow><mn>3</mn></mrow></msub><mo>,</mo><msub><mrow><mi>F</mi></mrow><mrow><mn>4</mn></mrow></msub><mo>)</mo></mrow></math></span>-partition. In this paper, we show that every planar graph without 4- and 6-cycles admits an <span><math><mrow><mo>(</mo><msub><mrow><mi>F</mi></mrow><mrow><mn>3</mn></mrow></msub><mo>,</mo><msub><mrow><mi>F</mi></mrow><mrow><mn>4</mn></mrow></msub><mo>)</mo></mrow></math></span>-partition, which strengthens a previous result due to Nakprasit et al. (2024) in a stronger form.</div></div>","PeriodicalId":50573,"journal":{"name":"Discrete Applied Mathematics","volume":"373 ","pages":"Pages 1-9"},"PeriodicalIF":1.0,"publicationDate":"2025-04-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143851792","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Two-disjoint-cycle-cover pancyclicity of augmented cubes
IF 1
3区 数学
Dongqin Cheng
{"title":"Two-disjoint-cycle-cover pancyclicity of augmented cubes","authors":"Dongqin Cheng","doi":"10.1016/j.dam.2025.04.033","DOIUrl":"10.1016/j.dam.2025.04.033","url":null,"abstract":"<div><div>A graph <span><math><mi>G</mi></math></span> is two-disjoint-cycle-cover <span><math><mrow><mo>[</mo><msub><mrow><mi>r</mi></mrow><mrow><mn>1</mn></mrow></msub><mo>,</mo><msub><mrow><mi>r</mi></mrow><mrow><mn>2</mn></mrow></msub><mo>]</mo></mrow></math></span>-pancyclic if there is a collection of two vertex disjoint cycles <span><math><mi>C</mi></math></span> of length <span><math><mrow><mi>l</mi><mrow><mo>(</mo><mi>C</mi><mo>)</mo></mrow></mrow></math></span> and <span><math><msup><mrow><mi>C</mi></mrow><mrow><mo>′</mo></mrow></msup></math></span> of length <span><math><mrow><mi>l</mi><mrow><mo>(</mo><msup><mrow><mi>C</mi></mrow><mrow><mo>′</mo></mrow></msup><mo>)</mo></mrow></mrow></math></span> such that <span><math><mrow><mi>l</mi><mrow><mo>(</mo><mi>C</mi><mo>)</mo></mrow><mo>+</mo><mi>l</mi><mrow><mo>(</mo><msup><mrow><mi>C</mi></mrow><mrow><mo>′</mo></mrow></msup><mo>)</mo></mrow><mo>=</mo><mrow><mo>|</mo><mi>V</mi><mrow><mo>(</mo><mi>G</mi><mo>)</mo></mrow><mo>|</mo></mrow></mrow></math></span> and <span><math><mrow><msub><mrow><mi>r</mi></mrow><mrow><mn>1</mn></mrow></msub><mo>≤</mo><mi>l</mi><mrow><mo>(</mo><mi>C</mi><mo>)</mo></mrow><mo>≤</mo><msub><mrow><mi>r</mi></mrow><mrow><mn>2</mn></mrow></msub></mrow></math></span>. The augmented cube is one of the variations of hypercube and possesses many good properties that the hypercube does not have. In this paper, we prove that the <span><math><mi>n</mi></math></span>-dimensional augmented cube <span><math><mrow><mi>A</mi><msub><mrow><mi>Q</mi></mrow><mrow><mi>n</mi></mrow></msub></mrow></math></span> is two-disjoint-cycle-cover <span><math><mrow><mo>[</mo><mn>3</mn><mo>,</mo><msup><mrow><mn>2</mn></mrow><mrow><mi>n</mi><mo>−</mo><mn>1</mn></mrow></msup><mo>]</mo></mrow></math></span>-pancyclic, where <span><math><mrow><mi>n</mi><mo>≥</mo><mn>3</mn></mrow></math></span>.</div></div>","PeriodicalId":50573,"journal":{"name":"Discrete Applied Mathematics","volume":"371 ","pages":"Pages 240-246"},"PeriodicalIF":1.0,"publicationDate":"2025-04-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143850568","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
影响因子
展开
类型
展开
期刊
展开
全部
Acc. Chem. Res.
ACS Applied Bio Materials
ACS Appl. Electron. Mater.
ACS Appl. Energy Mater.
ACS Appl. Mater. Interfaces
ACS Appl. Nano Mater.
ACS Appl. Polym. Mater.
ACS BIOMATER-SCI ENG
ACS Catal.
ACS Cent. Sci.
ACS Chem. Biol.
ACS Chemical Health & Safety
ACS Chem. Neurosci.
ACS Comb. Sci.
ACS Earth Space Chem.
ACS Energy Lett.
ACS Infect. Dis.
ACS Macro Lett.
ACS Mater. Lett.
ACS Med. Chem. Lett.
ACS Nano
ACS Omega
ACS Photonics
ACS Sens.
ACS Sustainable Chem. Eng.
ACS Synth. Biol.
Anal. Chem.
BIOCHEMISTRY-US
Bioconjugate Chem.
BIOMACROMOLECULES
Chem. Res. Toxicol.
Chem. Rev.
Chem. Mater.
CRYST GROWTH DES
ENERG FUEL
Environ. Sci. Technol.
Environ. Sci. Technol. Lett.
Eur. J. Inorg. Chem.
IND ENG CHEM RES
Inorg. Chem.
J. Agric. Food. Chem.
J. Chem. Eng. Data
J. Chem. Educ.
J. Chem. Inf. Model.
J. Chem. Theory Comput.
J. Med. Chem.
J. Nat. Prod.
J PROTEOME RES
J. Am. Chem. Soc.
LANGMUIR
MACROMOLECULES
Mol. Pharmaceutics
Nano Lett.
Org. Lett.
ORG PROCESS RES DEV
ORGANOMETALLICS
J. Org. Chem.
J. Phys. Chem.
J. Phys. Chem. A
J. Phys. Chem. B
J. Phys. Chem. C
J. Phys. Chem. Lett.
Analyst
Anal. Methods
Biomater. Sci.
Catal. Sci. Technol.
Chem. Commun.
Chem. Soc. Rev.
CHEM EDUC RES PRACT
CRYSTENGCOMM
Dalton Trans.
Energy Environ. Sci.
ENVIRON SCI-NANO
ENVIRON SCI-PROC IMP
ENVIRON SCI-WAT RES
Faraday Discuss.
Food Funct.
Green Chem.
Inorg. Chem. Front.
Integr. Biol.
J. Anal. At. Spectrom.
J. Mater. Chem. A
J. Mater. Chem. B
J. Mater. Chem. C
Lab Chip
Mater. Chem. Front.
Mater. Horiz.
MEDCHEMCOMM
Metallomics
Mol. Biosyst.
Mol. Syst. Des. Eng.
Nanoscale
Nanoscale Horiz.
Nat. Prod. Rep.
New J. Chem.
Org. Biomol. Chem.
Org. Chem. Front.
PHOTOCH PHOTOBIO SCI
PCCP
Polym. Chem.
×
引用
GB/T 7714-2015
复制
MLA
复制
APA
复制
导出至
BibTeX
EndNote
RefMan
NoteFirst
NoteExpress
求助内容：
应助结果提醒方式：请完成安全验证×
京公网安备 11010802042870号
