Stephen Kirkland , Yuqiao Li , John S. McAlister , Xiaohong Zhang
{"title":"Edge addition and the change in Kemeny’s constant","authors":"Stephen Kirkland , Yuqiao Li , John S. McAlister , Xiaohong Zhang","doi":"10.1016/j.dam.2025.04.031","DOIUrl":"10.1016/j.dam.2025.04.031","url":null,"abstract":"<div><div>Given a connected graph <span><math><mi>G</mi></math></span>, Kemeny’s constant <span><math><mrow><mi>K</mi><mrow><mo>(</mo><mi>G</mi><mo>)</mo></mrow></mrow></math></span> measures the average travel time for a random walk to reach a randomly selected vertex. It is known that when an edge is added to <span><math><mi>G</mi></math></span>, the value of Kemeny’s constant may either decrease, increase, or stay the same. In this paper, we present a quantitative analysis of this behaviour when the initial graph is a tree with <span><math><mi>n</mi></math></span> vertices. We prove that when an edge is added into a tree on <span><math><mi>n</mi></math></span> vertices, the maximum possible increase in Kemeny’s constant is roughly <span><math><mrow><mfrac><mrow><mn>2</mn></mrow><mrow><mn>3</mn></mrow></mfrac><mi>n</mi><mo>,</mo></mrow></math></span> while the maximum possible decrease is roughly <span><math><mrow><mfrac><mrow><mn>3</mn></mrow><mrow><mn>16</mn></mrow></mfrac><msup><mrow><mi>n</mi></mrow><mrow><mn>2</mn></mrow></msup></mrow></math></span>. We also identify the trees, and the edges to be added, that correspond to the maximum increase and maximum decrease. Throughout, both matrix theoretic and graph theoretic techniques are employed.</div></div>","PeriodicalId":50573,"journal":{"name":"Discrete Applied Mathematics","volume":"373 ","pages":"Pages 77-90"},"PeriodicalIF":1.0,"publicationDate":"2025-04-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143870013","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}
{"title":"On cubic rainbow domination regular graphs","authors":"Boštjan Kuzman","doi":"10.1016/j.dam.2025.04.046","DOIUrl":"10.1016/j.dam.2025.04.046","url":null,"abstract":"<div><div>A <span><math><mi>d</mi></math></span>-regular graph <span><math><mi>X</mi></math></span> is called <span><math><mi>d</mi></math></span>-rainbow domination regular or <span><math><mi>d</mi></math></span>-RDR, if its <span><math><mi>d</mi></math></span>-rainbow domination number <span><math><mrow><msub><mrow><mi>γ</mi></mrow><mrow><mi>r</mi><mi>d</mi></mrow></msub><mrow><mo>(</mo><mi>X</mi><mo>)</mo></mrow></mrow></math></span> attains the lower bound <span><math><mrow><mi>n</mi><mo>/</mo><mn>2</mn></mrow></math></span> for <span><math><mi>d</mi></math></span>-regular graphs, where <span><math><mi>n</mi></math></span> is the number of vertices. In the paper, two combinatorial constructions to construct new <span><math><mi>d</mi></math></span>-RDR graphs from existing ones are described and two general criteria for a vertex-transitive <span><math><mi>d</mi></math></span>-regular graph to be <span><math><mi>d</mi></math></span>-RDR are proven. A list of vertex-transitive 3-RDR graphs of small orders is produced and their partial classification into families of generalized Petersen graphs, honeycomb-toroidal graphs and a specific family of Cayley graphs is given by investigating the girth and local cycle structure of these graphs.</div></div>","PeriodicalId":50573,"journal":{"name":"Discrete Applied Mathematics","volume":"373 ","pages":"Pages 26-38"},"PeriodicalIF":1.0,"publicationDate":"2025-04-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143870010","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}
{"title":"Several classes of minimal linear codes from weakly regular and non-weakly regular bent functions","authors":"Wengang Jin, Kangquan Li, Longjiang Qu","doi":"10.1016/j.dam.2025.04.044","DOIUrl":"10.1016/j.dam.2025.04.044","url":null,"abstract":"<div><div>As a special subclass of linear codes, minimal linear codes have attracted considerable attention in coding theory and cryptography due to their significant applications in secret sharing schemes and secure two-party computation. In this paper, we are devoted to constructing minimal linear codes violating the Ashikhmin–Barg (AB for short) condition over finite fields of odd characteristic. First, we present several classes of minimal linear codes violating the AB condition from weakly regular bent functions and determine their weight distributions. Next, we construct four to six weights minimal linear codes violating the AB condition by using non-weakly regular bent functions. Meanwhile, their weight distributions are also provided. To the best of our knowledge, this paper is the first one to investigate the constructions of minimal linear codes that violate the AB condition by using both weakly regular and non-weakly regular bent functions over finite fields of odd characteristic.</div></div>","PeriodicalId":50573,"journal":{"name":"Discrete Applied Mathematics","volume":"373 ","pages":"Pages 53-76"},"PeriodicalIF":1.0,"publicationDate":"2025-04-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143870012","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}
Yuanfen Song , Yuxia Li , Maurizio Brunetti , Jianfeng Wang
{"title":"On the third largest eigenvalue of eccentricity matrices of graphs","authors":"Yuanfen Song , Yuxia Li , Maurizio Brunetti , Jianfeng Wang","doi":"10.1016/j.dam.2025.04.039","DOIUrl":"10.1016/j.dam.2025.04.039","url":null,"abstract":"<div><div>Let <span><math><mrow><mi>D</mi><mrow><mo>(</mo><mi>G</mi><mo>)</mo></mrow></mrow></math></span> denote the distance matrix of a connected graph <span><math><mi>G</mi></math></span>. The eccentricity matrix (or anti-adjacency matrix) of <span><math><mi>G</mi></math></span> is obtained from <span><math><mrow><mi>D</mi><mrow><mo>(</mo><mi>G</mi><mo>)</mo></mrow></mrow></math></span> by retaining in each row and each column only the maximal entries. In this paper, all the graphs with third largest eccentricity eigenvalue in the interval <span><math><mrow><mo>(</mo><mo>−</mo><mn>1</mn><mo>,</mo><mn>0</mn><mo>)</mo></mrow></math></span> are detected. It turns out that these graphs are all found among the chain graphs with (nonempty) four cells and the graphs of type <span><math><mrow><msub><mrow><mi>K</mi></mrow><mrow><mi>t</mi></mrow></msub><mo>∨</mo><mrow><mo>(</mo><mi>G</mi><mo>∪</mo><mi>k</mi><msub><mrow><mi>K</mi></mrow><mrow><mn>1</mn></mrow></msub><mo>)</mo></mrow></mrow></math></span>, where <span><math><mrow><mi>k</mi><mo>⩾</mo><mn>0</mn></mrow></math></span> and <span><math><mi>G</mi></math></span> is a chain graph with at most ten cells.</div></div>","PeriodicalId":50573,"journal":{"name":"Discrete Applied Mathematics","volume":"372 ","pages":"Pages 237-259"},"PeriodicalIF":1.0,"publicationDate":"2025-04-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143869704","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}
{"title":"Nordhaus–Gaddum-type results for monitoring edge-geodetic number of graphs","authors":"Yingying Zhang , Fanfan Wang , Chenxu Yang","doi":"10.1016/j.dam.2025.04.040","DOIUrl":"10.1016/j.dam.2025.04.040","url":null,"abstract":"<div><div>Inspired by two notions (distance-edge-monitoring set and edge-geodetic set), Foucaud et al. introduced the concept of monitoring edge-geodetic set, which is used to monitor the links of a network in order to detect and prevent failures. A vertex set of a graph is called a <em>monitoring edge-geodetic set</em> (<em>MEG-set</em> for short) if the removal of any edge changes the distance between some pair of vertices in the set. The cardinality of the minimum monitoring edge-geodetic set is called the <em>monitoring edge-geodetic number</em>. In this paper, we give Nordhaus–Gaddum-type results of general graphs, trees and unicyclic graphs with respect to monitoring edge-geodetic number. Moreover, we characterize the extremal graphs, which reach the bounds.</div></div>","PeriodicalId":50573,"journal":{"name":"Discrete Applied Mathematics","volume":"373 ","pages":"Pages 39-52"},"PeriodicalIF":1.0,"publicationDate":"2025-04-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143870011","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}
{"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}
{"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}
{"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}
{"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}
{"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}
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