Discrete Applied Mathematics最新文献_第2页

The thickness of a graph with constraint on girth 有周长约束的图的厚度

IF 1 3区数学

Discrete Applied Mathematics Pub Date : 2025-07-26 DOI: 10.1016/j.dam.2025.07.025

Dengju Ma

引用次数: 0

Intersection of cycles and paths in k-connected graphs k连通图中环与路径的交

IF 1 3区数学

Discrete Applied Mathematics Pub Date : 2025-07-25 DOI: 10.1016/j.dam.2025.07.013

Haidong Wu

引用次数: 0

Characterization of graphs with orientable total domination number equal to |V|−1 可定向总控制数等于|V|−1的图的表征

IF 1 3区数学

Discrete Applied Mathematics Pub Date : 2025-07-25 DOI: 10.1016/j.dam.2025.07.021

Zoltán L. Blázsik , Leila Vivien Nagy

引用次数: 0

On the independence polynomial and threshold of an antiregular k-hypergraph 反正则k超图的独立多项式和阈值

IF 1 3区数学

Discrete Applied Mathematics Pub Date : 2025-07-25 DOI: 10.1016/j.dam.2025.07.017

Erchuan Zhang

{"title":"On the independence polynomial and threshold of an antiregular k-hypergraph","authors":"Erchuan Zhang","doi":"10.1016/j.dam.2025.07.017","DOIUrl":"10.1016/j.dam.2025.07.017","url":null,"abstract":"<div><div>Given an integer <math><mrow><mi>k</mi><mo>≥</mo><mn>3</mn></mrow></math> and initial <math><mrow><mi>k</mi><mo>−</mo><mn>1</mn></mrow></math> isolated vertices, an antiregular <math><mi>k</mi></math>-hypergraph is constructed by alternatively adding an isolated vertex (connected to no other vertices) or a dominating vertex (connected to every other <math><mrow><mi>k</mi><mo>−</mo><mn>1</mn></mrow></math> vertices). Let <math><msub><mrow><mi>a</mi></mrow><mrow><mi>i</mi></mrow></msub></math> be the number of independent sets of cardinality <math><mi>i</mi></math> in a hypergraph <math><mi>H</mi></math>, then the independence polynomial of <math><mi>H</mi></math> is defined as <math><mrow><mi>I</mi><mrow><mo>(</mo><mi>H</mi><mo>;</mo><mi>x</mi><mo>)</mo></mrow><mo>=</mo><msubsup><mrow><mo>∑</mo></mrow><mrow><mi>i</mi><mo>=</mo><mn>0</mn></mrow><mrow><mi>m</mi></mrow></msubsup><msub><mrow><mi>a</mi></mrow><mrow><mi>i</mi></mrow></msub><msup><mrow><mi>x</mi></mrow><mrow><mi>i</mi></mrow></msup></mrow></math>, where <math><mi>m</mi></math> is the size of a maximum independent set. The main purpose of the present paper is to generalize some results of independence polynomials of antiregular graphs to the case of antiregular <math><mi>k</mi></math>-hypergraphs. In particular, we derive (semi-)closed formulas for the independence polynomials of antiregular <math><mi>k</mi></math>-hypergraphs and prove their log-concavity. Furthermore, we show that antiregular <math><mi>k</mi></math>-hypergraphs are <math><mrow><mi>T</mi><mn>2</mn></mrow></math>-threshold, which means there exist a labeling <math><mi>c</mi></math> of the vertex set and a threshold <math><mi>τ</mi></math> such that for any vertex subset <math><mi>S</mi></math> of cardinality <math><mi>k</mi></math>, <math><mrow><msub><mrow><mo>∑</mo></mrow><mrow><mi>i</mi><mo>∈</mo><mi>S</mi></mrow></msub><mi>c</mi><mrow><mo>(</mo><mi>i</mi><mo>)</mo></mrow><mo>></mo><mi>τ</mi></mrow></math> if and only if <math><mi>S</mi></math> is a hyperedge.</div></div>","PeriodicalId":50573,"journal":{"name":"Discrete Applied Mathematics","volume":"378 ","pages":"Pages 244-258"},"PeriodicalIF":1.0,"publicationDate":"2025-07-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144703916","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

Characterizing and computing in linear time mutual-visibility parameters in distance-hereditary graphs 距离遗传图中线性时间互可视性参数的刻画与计算

IF 1 3区数学

Discrete Applied Mathematics Pub Date : 2025-07-25 DOI: 10.1016/j.dam.2025.07.026

Serafino Cicerone, Gabriele Di Stefano

{"title":"Characterizing and computing in linear time mutual-visibility parameters in distance-hereditary graphs","authors":"Serafino Cicerone, Gabriele Di Stefano","doi":"10.1016/j.dam.2025.07.026","DOIUrl":"10.1016/j.dam.2025.07.026","url":null,"abstract":"<div><div>The mutual-visibility problem in a graph <math><mi>G</mi></math> asks for the cardinality of a largest set of vertices <math><mrow><mi>X</mi><mo>⊆</mo><mi>V</mi><mrow><mo>(</mo><mi>G</mi><mo>)</mo></mrow></mrow></math> so that for any two vertices <math><mrow><mi>x</mi><mo>,</mo><mi>y</mi><mo>∈</mo><mi>X</mi></mrow></math> there is a shortest <math><mrow><mi>x</mi><mo>,</mo><mi>y</mi></mrow></math>-path whose internal vertices are all not in <math><mi>X</mi></math>. Variations of this problem are known, based on the extension of the visibility property of vertices that are in and/or outside <math><mi>X</mi></math>. It is known that solving the mutual-visibility problem in all its variations is NP-complete, whereas it has been shown that there are exact formulas for special graph classes like paths, cycles, blocks, cographs, and for the Cartesian product of some simple graphs like paths, cliques and cycles.</div><div>In this paper, we study the (variations of) mutual-visibility problem in the context of distance-hereditary graphs. In particular, we introduce the direct canonical decomposition of a graph as a tool for defining useful structural properties of the graphs studied. Then, we show that such properties allow us to devise a linear-time algorithm for solving all the variants of the mutual-visibility problem for distance-hereditary graphs. In turn, this allowed us to show that a recently posed conjecture about the total mutual-visibility number of distance-hereditary graphs holds.</div></div>","PeriodicalId":50573,"journal":{"name":"Discrete Applied Mathematics","volume":"376 ","pages":"Pages 359-373"},"PeriodicalIF":1.0,"publicationDate":"2025-07-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144702915","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

Minimum embedded-link-cut split k-ary n-cubes 最小嵌入链切分割k-ary n-立方体

IF 1 3区数学

Discrete Applied Mathematics Pub Date : 2025-07-25 DOI: 10.1016/j.dam.2025.07.031

Yuxing Yang, Kaiyue Meng

引用次数: 0

An infinite family of normal 5-edge colorable superpositioned snarks 一个无限族的正常的5边可着色叠加的缠结

IF 1 3区数学

Discrete Applied Mathematics Pub Date : 2025-07-25 DOI: 10.1016/j.dam.2025.07.032

Wenjuan Zhou , Rong-Xia Hao , Rong Luo , Yilun Luo

{"title":"An infinite family of normal 5-edge colorable superpositioned snarks","authors":"Wenjuan Zhou , Rong-Xia Hao , Rong Luo , Yilun Luo","doi":"10.1016/j.dam.2025.07.032","DOIUrl":"10.1016/j.dam.2025.07.032","url":null,"abstract":"<div><div>Let <math><mi>G</mi></math> be a cubic graph. For a proper edge coloring <math><mi>π</mi></math> of <math><mi>G</mi></math>, an edge <math><mrow><mi>e</mi><mo>∈</mo><mi>E</mi><mrow><mo>(</mo><mi>G</mi><mo>)</mo></mrow></mrow></math> is normal if the number of colors of all edges incident to endvertices of <math><mi>e</mi></math> is 3 or 5. A normal <math><mi>k</mi></math>-edge coloring of <math><mi>G</mi></math> is a proper edge coloring with <math><mi>k</mi></math> colors such that each edge of <math><mi>G</mi></math> is normal. The normal chromatic index of <math><mi>G</mi></math>, denoted by <math><mrow><msubsup><mrow><mi>χ</mi></mrow><mrow><mi>N</mi></mrow><mrow><mo>′</mo></mrow></msubsup><mrow><mo>(</mo><mi>G</mi><mo>)</mo></mrow></mrow></math>, is the smallest integer <math><mi>k</mi></math> such that <math><mi>G</mi></math> admits a normal <math><mi>k</mi></math>-edge coloring. Jaeger conjectured that <math><mrow><msubsup><mrow><mi>χ</mi></mrow><mrow><mi>N</mi></mrow><mrow><mo>′</mo></mrow></msubsup><mrow><mo>(</mo><mi>G</mi><mo>)</mo></mrow><mo>≤</mo><mn>5</mn></mrow></math> for every bridgeless cubic graph <math><mi>G</mi></math>, and he also proved that this conjecture is equivalent to the Petersen coloring conjecture. The normal 5-edge coloring conjecture has been verified for some families of snarks, such as, generalized Blanuša snarks, Goldberg snarks, flower snarks and Loupekhine snarks. Sedlar et al. proved that this conjecture holds for two families of superpositioned snarks. In this paper, we present a construction of superpositioned snarks whose normal chromatic indices equal to 5, which implies the normal 5-edge coloring conjecture for large families of snarks.</div></div>","PeriodicalId":50573,"journal":{"name":"Discrete Applied Mathematics","volume":"378 ","pages":"Pages 259-269"},"PeriodicalIF":1.0,"publicationDate":"2025-07-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144703915","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

Signless Laplacian energy and spectral radius of a graph 图的无符号拉普拉斯能量和谱半径

IF 1 3区数学

Discrete Applied Mathematics Pub Date : 2025-07-25 DOI: 10.1016/j.dam.2025.07.015

Yuanyuan Chen , Shuting Liu , Zhiwen Wang

{"title":"Signless Laplacian energy and spectral radius of a graph","authors":"Yuanyuan Chen , Shuting Liu , Zhiwen Wang","doi":"10.1016/j.dam.2025.07.015","DOIUrl":"10.1016/j.dam.2025.07.015","url":null,"abstract":"<div><div>For a graph <math><mi>G</mi></math>, the signless Laplacian energy is defined as <math><mrow><msup><mrow><mi>E</mi></mrow><mrow><mi>Q</mi></mrow></msup><mrow><mo>(</mo><mi>G</mi><mo>)</mo></mrow><mo>=</mo><msubsup><mrow><mo>∑</mo></mrow><mrow><mi>i</mi><mo>=</mo><mn>1</mn></mrow><mrow><mi>n</mi></mrow></msubsup><mfenced><mrow><msub><mrow><mi>q</mi></mrow><mrow><mi>i</mi></mrow></msub><mo>−</mo><mfrac><mrow><mn>2</mn><mi>m</mi></mrow><mrow><mi>n</mi></mrow></mfrac></mrow></mfenced></mrow></math>, where <math><mi>n</mi></math> and <math><mi>m</mi></math> are the order and the size, and <math><msub><mrow><mi>q</mi></mrow><mrow><mi>i</mi></mrow></msub></math> is the <math><mi>i</mi></math>th largest signless Laplacian eigenvalue of <math><mi>G</mi></math>, respectively. In this paper, we establish a sharp lower bound of the signless Laplacian spectral radius of a graph <math><mi>G</mi></math> in terms of the degree and the average 2-degree, generalizing a well-known lower bound that <math><mrow><msub><mrow><mi>q</mi></mrow><mrow><mn>1</mn></mrow></msub><mo>≥</mo><mi>Δ</mi><mo>+</mo><mn>1</mn></mrow></math>. As applications, we give sharp lower and upper bounds of its signless Laplacian energy for a connected graph and a bipartite graph. All extremal graphs involved are characterized.</div></div>","PeriodicalId":50573,"journal":{"name":"Discrete Applied Mathematics","volume":"378 ","pages":"Pages 216-225"},"PeriodicalIF":1.0,"publicationDate":"2025-07-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144703910","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

The size and the spectral radius of a saturated non-covered graph 饱和无覆盖图的大小和谱半径

IF 1 3区数学

Discrete Applied Mathematics Pub Date : 2025-07-23 DOI: 10.1016/j.dam.2025.07.029

Zeyuan Wu , Hongzhang Chen , Jianxi Li

{"title":"The size and the spectral radius of a saturated non-covered graph","authors":"Zeyuan Wu , Hongzhang Chen , Jianxi Li","doi":"10.1016/j.dam.2025.07.029","DOIUrl":"10.1016/j.dam.2025.07.029","url":null,"abstract":"<div><div>A graph <math><mrow><mi>G</mi><mo>=</mo><mrow><mo>(</mo><mi>V</mi><mo>,</mo><mi>E</mi><mo>)</mo></mrow></mrow></math> is a matching-covered graph if for every <math><mrow><mi>e</mi><mo>∈</mo><mi>E</mi><mrow><mo>(</mo><mi>G</mi><mo>)</mo></mrow></mrow></math>, there exists at least one perfect matching <math><mi>M</mi></math> of <math><mi>G</mi></math> such that <math><mrow><mi>e</mi><mo>∈</mo><mi>M</mi></mrow></math>. A graph <math><mi>G</mi></math> of even order is a saturated non-covered graph if for any <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>, <math><mrow><mi>G</mi><mo>+</mo><mi>e</mi></mrow></math> is a matching-covered graph but <math><mi>G</mi></math> is not. Very recently, Zhou, Cao and Yan (2025) provided a structural characterization on the saturated non-covered graphs. In this paper, we further study the saturated non-covered graph from its size and eigenvalues. The graphs with the maximum size and the maximum spectral radius among all saturated non-covered graphs are identified, respectively, as well as an upper bound on the Laplacian eigenratio of a saturated non-covered graph is also established.</div></div>","PeriodicalId":50573,"journal":{"name":"Discrete Applied Mathematics","volume":"377 ","pages":"Pages 343-349"},"PeriodicalIF":1.0,"publicationDate":"2025-07-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144687271","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 adjacency lemma on signed edge colorings with an application to planar graphs 符号边着色的邻接引理及其在平面图上的应用

IF 1 3区数学

Discrete Applied Mathematics Pub Date : 2025-07-23 DOI: 10.1016/j.dam.2025.07.024

Li Zhang , Hajo Broersma , You Lu , Shenggui Zhang

引用次数: 0