Discrete Applied Mathematics最新文献_第10页

Classification of borderenergetic chemical graphs and borderenergetic graphs of order 12 边能化学图和12阶边能图的分类

IF 1 3区数学

Discrete Applied Mathematics Pub Date : 2025-07-31 DOI: 10.1016/j.dam.2025.07.035

Péter Csikvári , Ivan Damnjanović , Marko Milošević , Ivan Stanković , Dragan Stevanović

{"title":"Classification of borderenergetic chemical graphs and borderenergetic graphs of order 12","authors":"Péter Csikvári , Ivan Damnjanović , Marko Milošević , Ivan Stanković , Dragan Stevanović","doi":"10.1016/j.dam.2025.07.035","DOIUrl":"10.1016/j.dam.2025.07.035","url":null,"abstract":"<div><div>The energy <math><mrow><mi>E</mi><mrow><mo>(</mo><mi>G</mi><mo>)</mo></mrow></mrow></math> of a simple graph <math><mi>G</mi></math> is the sum of absolute values of the eigenvalues of its adjacency matrix. A borderenergetic graph of order <math><mrow><mi>n</mi><mo>∈</mo><mi>N</mi></mrow></math> is any noncomplete graph <math><mi>G</mi></math> such that <math><mrow><mi>E</mi><mrow><mo>(</mo><mi>G</mi><mo>)</mo></mrow><mo>=</mo><mi>E</mi><mrow><mo>(</mo><msub><mrow><mi>K</mi></mrow><mrow><mi>n</mi></mrow></msub><mo>)</mo></mrow><mo>=</mo><mn>2</mn><mi>n</mi><mo>−</mo><mn>2</mn></mrow></math>. Here we combine two-phase computer-assisted search with theoretical arguments to show that there are only three borderenergetic chemical graphs, thus completing the earlier findings of Li et al. (2017). We perform two-phase computer-assisted search to also find all 566 borderenergetic graphs of order 12, thereby correcting and extending the results from a previous search performed by Furtula and Gutman (2017).</div></div>","PeriodicalId":50573,"journal":{"name":"Discrete Applied Mathematics","volume":"376 ","pages":"Pages 394-403"},"PeriodicalIF":1.0,"publicationDate":"2025-07-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144750450","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

Scheduling sports tournaments with two court types 安排两种场地类型的体育比赛

IF 1 3区数学

Discrete Applied Mathematics Pub Date : 2025-07-30 DOI: 10.1016/j.dam.2025.07.018

Sigrid Knust , Melissa Koch , Xuan Thanh Le

引用次数: 0

Corrigendum to: “On Ramsey and star-critical Ramsey numbers for generalized fans versus nKm” [Discrete Appl. Math. 305 (2021) 64–70] 《关于广义粉丝与nKm的拉姆齐和明星临界拉姆齐数》的勘误表[离散应用]。数学。305 (2021)64-70]

IF 1 3区数学

Discrete Applied Mathematics Pub Date : 2025-07-30 DOI: 10.1016/j.dam.2025.07.023

Arran Hamm, Paul Hazelton, Suzanna Thompson

引用次数: 0

The edge metric dimensions of convex polytopes 凸多面体的边缘度量尺寸

IF 1 3区数学

Discrete Applied Mathematics Pub Date : 2025-07-30 DOI: 10.1016/j.dam.2025.07.027

Meiqin Wei , Bohua Fan , Changhong Lu , Jun Yue , Jinfeng Liu

{"title":"The edge metric dimensions of convex polytopes","authors":"Meiqin Wei , Bohua Fan , Changhong Lu , Jun Yue , Jinfeng Liu","doi":"10.1016/j.dam.2025.07.027","DOIUrl":"10.1016/j.dam.2025.07.027","url":null,"abstract":"<div><div>Let <math><mrow><mi>G</mi><mo>=</mo><mrow><mo>(</mo><mi>V</mi><mo>,</mo><mi>E</mi><mo>)</mo></mrow></mrow></math> be a connected graph. A vertex <math><mrow><mi>x</mi><mo>∈</mo><mi>V</mi></mrow></math> distinguishes the edge pair <math><mrow><msub><mrow><mi>e</mi></mrow><mrow><mn>1</mn></mrow></msub><mo>,</mo><msub><mrow><mi>e</mi></mrow><mrow><mn>2</mn></mrow></msub><mo>∈</mo><mi>E</mi></mrow></math> if the distances from <math><mi>x</mi></math> to <math><msub><mrow><mi>e</mi></mrow><mrow><mn>1</mn></mrow></msub></math> and <math><msub><mrow><mi>e</mi></mrow><mrow><mn>2</mn></mrow></msub></math> are distinct. A vertex subset <math><mrow><mi>S</mi><mo>⊆</mo><mi>V</mi></mrow></math> is an edge metric generator of <math><mi>G</mi></math> if any pair of edges in <math><mi>E</mi></math> can be distinguished by some element of <math><mi>S</mi></math>. The minimum size of an edge metric generator of <math><mi>G</mi></math> is called the edge metric dimension of <math><mi>G</mi></math> and denoted by <math><mrow><mi>e</mi><mi>d</mi><mi>i</mi><mi>m</mi><mrow><mo>(</mo><mi>G</mi><mo>)</mo></mrow></mrow></math>. In this paper, we determine the exact values of the edge metric dimensions for some convex polytopes and generalized convex polytopes, which further emphasize the fact that there are families of convex polytopes having greater edge metric dimensions than their metric dimensions. The proof methods in this paper are constructive and they can be implemented through algorithms.</div></div>","PeriodicalId":50573,"journal":{"name":"Discrete Applied Mathematics","volume":"378 ","pages":"Pages 294-306"},"PeriodicalIF":1.0,"publicationDate":"2025-07-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144724344","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 k-matching, k-factor-critical and Aα-spectral radius 完美的k匹配，k因子临界和a α谱半径

IF 1 3区数学

Discrete Applied Mathematics Pub Date : 2025-07-29 DOI: 10.1016/j.dam.2025.07.020

Mengyuan Niu , Shanshan Zhang , Xiumei Wang

引用次数: 0

Sequential testing problem: A follow-up review 顺序测试问题：后续审查

IF 1 3区数学

Discrete Applied Mathematics Pub Date : 2025-07-28 DOI: 10.1016/j.dam.2025.07.039

Tonguç Ünlüyurt

引用次数: 0

About the infinite windy firebreak location problem 关于无限风防火墙的选址问题

IF 1 3区数学

Discrete Applied Mathematics Pub Date : 2025-07-28 DOI: 10.1016/j.dam.2025.07.028

Marc Demange , Alessia Di Fonso , Gabriele Di Stefano , Pierpaolo Vittorini

{"title":"About the infinite windy firebreak location problem","authors":"Marc Demange , Alessia Di Fonso , Gabriele Di Stefano , Pierpaolo Vittorini","doi":"10.1016/j.dam.2025.07.028","DOIUrl":"10.1016/j.dam.2025.07.028","url":null,"abstract":"<div><div>The severity of wildfires can be mitigated using preventive measures like the construction of firebreaks, which are strips of land from which the vegetation is completely removed. In this paper, we model the problem of wildfire containment as an optimization problem on infinite graphs called Infinite Windy Firebreak Location. A land of unknown size is modeled as an infinite undirected graph in which the vertices correspond to areas subject to fire and edges represent fire propagation from one area to another. A firebreak construction is modeled as removing the edge between two vertices. The number of firebreaks that can be installed depends on budget constraints. We assume that a fire ignites in a subset of vertices and propagates to the neighbors. The goal is to select a subset of edges to remove in order to contain the fire and avoid burning an infinite part of the graph. We prove that Infinite Windy Firebreak Location is coNP-complete in restricted cases, and we address some polynomial cases. We show that Infinite Windy Firebreak Location polynomially reduces to Min Cut for certain classes of graphs like infinite grid graphs and polyomino-grids.</div></div>","PeriodicalId":50573,"journal":{"name":"Discrete Applied Mathematics","volume":"378 ","pages":"Pages 280-293"},"PeriodicalIF":1.0,"publicationDate":"2025-07-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144714080","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

A note on obtaining bipartite radio graceful graphs of arbitrarily large radio numbers with radio graceful complements 关于获得具有任意大无线电数的无线电优美补的二部无线电优美图的注记

IF 1 3区数学

Discrete Applied Mathematics Pub Date : 2025-07-28 DOI: 10.1016/j.dam.2025.07.012

Ushnish Sarkar

{"title":"A note on obtaining bipartite radio graceful graphs of arbitrarily large radio numbers with radio graceful complements","authors":"Ushnish Sarkar","doi":"10.1016/j.dam.2025.07.012","DOIUrl":"10.1016/j.dam.2025.07.012","url":null,"abstract":"<div><div>Motivated by the frequency assignment problem (FAP), a radio coloring of a graph <math><mi>G</mi></math> is an assignment <math><mi>f</mi></math> of non-negative integers to the vertices of <math><mi>G</mi></math> satisfying the condition <math><mrow><mrow><mo>|</mo><mi>f</mi><mrow><mo>(</mo><mi>u</mi><mo>)</mo></mrow><mo>−</mo><mi>f</mi><mrow><mo>(</mo><mi>v</mi><mo>)</mo></mrow><mo>|</mo></mrow><mo>+</mo><mi>d</mi><mrow><mo>(</mo><mi>u</mi><mo>,</mo><mi>v</mi><mo>)</mo></mrow><mo>≥</mo><mtext>diameter of</mtext><mspace></mspace><mi>G</mi><mo>+</mo><mn>1</mn></mrow></math>, where <math><mrow><mi>d</mi><mrow><mo>(</mo><mi>u</mi><mo>,</mo><mi>v</mi><mo>)</mo></mrow></mrow></math> is the distance between any two vertices <math><mi>u</mi></math> and <math><mi>v</mi></math> of the graph <math><mi>G</mi></math>. The span of a radio coloring of <math><mi>G</mi></math> is the difference of the maximum and minimum non-negative integers used as colors. The minimum span of a radio coloring of <math><mi>G</mi></math> is referred as the radio number of <math><mi>G</mi></math>. Any radio coloring with the minimum span is referred as an optimal radio coloring of <math><mi>G</mi></math>. If an optimal radio coloring of <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 bijection from <math><mi>V</mi></math> to <math><mrow><mo>{</mo><mn>0</mn><mo>,</mo><mspace></mspace><mn>1</mn><mo>,</mo><mspace></mspace><mo>…</mo><mo>,</mo><mspace></mspace><mrow><mo>|</mo><mi>V</mi><mo>|</mo></mrow><mo>−</mo><mn>1</mn><mo>}</mo></mrow></math>, then the graph is referred as radio graceful. In this article, using a recursive construction, we have shown that for each positive integer <math><mrow><mi>n</mi><mo>≥</mo><mn>9</mn></mrow></math>, there exists a bipartite graph <math><msub><mrow><mi>G</mi></mrow><mrow><mi>n</mi></mrow></msub></math> with <math><mrow><mi>n</mi><mo>+</mo><mn>1</mn></mrow></math> vertices such that both <math><msub><mrow><mi>G</mi></mrow><mrow><mi>n</mi></mrow></msub></math> and its complement <math><msubsup><mrow><mi>G</mi></mrow><mrow><mi>n</mi></mrow><mrow><mi>c</mi></mrow></msubsup></math> are radio graceful graphs. In the process, we show that each such <math><msub><mrow><mi>G</mi></mrow><mrow><mi>n</mi></mrow></msub></math> and <math><msubsup><mrow><mi>G</mi></mrow><mrow><mi>n</mi></mrow><mrow><mi>c</mi></mrow></msubsup></math> contain a Hamiltonian path.</div><div>Note that our construction obtains radio graceful graphs of arbitrarily large radio numbers without going for big cliques. This has an interesting similarity with the motivation behind the Mycielski’s construction which ensures the exis","PeriodicalId":50573,"journal":{"name":"Discrete Applied Mathematics","volume":"377 ","pages":"Pages 350-355"},"PeriodicalIF":1.0,"publicationDate":"2025-07-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144712954","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 novel minimax results for perfect matchings of polyomino graphs 多项式图完美匹配的一些新颖的极大极小结果

IF 1 3区数学

Discrete Applied Mathematics Pub Date : 2025-07-28 DOI: 10.1016/j.dam.2025.07.030

Chunhu Sun , Heping Zhang

{"title":"Some novel minimax results for perfect matchings of polyomino graphs","authors":"Chunhu Sun , Heping Zhang","doi":"10.1016/j.dam.2025.07.030","DOIUrl":"10.1016/j.dam.2025.07.030","url":null,"abstract":"<div><div>Let <math><mi>G</mi></math> be a graph with a perfect matching <math><mi>M</mi></math>. The forcing number of <math><mi>M</mi></math> in <math><mi>G</mi></math>, denoted by <math><mrow><mi>f</mi><mrow><mo>(</mo><mi>G</mi><mo>,</mo><mi>M</mi><mo>)</mo></mrow></mrow></math>, is the minimal size of an edge subset of <math><mi>M</mi></math> that are contained in no other perfect matchings of <math><mi>G</mi></math>, and the anti-forcing number of <math><mi>M</mi></math> in <math><mi>G</mi></math>, denoted by <math><mrow><mi>a</mi><mi>f</mi><mrow><mo>(</mo><mi>G</mi><mo>,</mo><mi>M</mi><mo>)</mo></mrow></mrow></math>, is the minimal size of an edge subset of <math><mrow><mi>E</mi><mrow><mo>(</mo><mi>G</mi><mo>)</mo></mrow></mrow></math> whose deletion results in a subgraph with a unique perfect matching <math><mi>M</mi></math>. For a polyomino graph <math><mi>P</mi></math>, Zhou and Zhang (2016) established a minimax result: For every perfect matching <math><mi>M</mi></math> of <math><mi>P</mi></math> with the maximum forcing number or minus one, <math><mrow><mi>f</mi><mrow><mo>(</mo><mi>P</mi><mo>,</mo><mi>M</mi><mo>)</mo></mrow></mrow></math> is equal to the maximum number of disjoint <math><mi>M</mi></math>-alternating squares in <math><mi>P</mi></math>. In this paper, we show that for every perfect matching <math><mi>M</mi></math> of a polyomino graph <math><mi>P</mi></math> which contains no 3 × 3 chessboard as a nice subgraph, <math><mrow><mi>f</mi><mrow><mo>(</mo><mi>P</mi><mo>,</mo><mi>M</mi><mo>)</mo></mrow></mrow></math> is equal to the maximum number of disjoint <math><mi>M</mi></math>-alternating squares in <math><mi>P</mi></math>. Further we show that for every perfect matching <math><mi>M</mi></math> of <math><mi>P</mi></math>, <math><mrow><mi>a</mi><mi>f</mi><mrow><mo>(</mo><mi>P</mi><mo>,</mo><mi>M</mi><mo>)</mo></mrow></mrow></math> always equals the number of <math><mi>M</mi></math>-alternating squares of <math><mi>P</mi></math> if and only if <math><mi>P</mi></math> has no 1 × 3 chessboard as a nice subgraph.</div></div>","PeriodicalId":50573,"journal":{"name":"Discrete Applied Mathematics","volume":"378 ","pages":"Pages 270-279"},"PeriodicalIF":1.0,"publicationDate":"2025-07-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144714079","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

On z-coloring and b∗-coloring of graphs as improved variants of the b-coloring 图的z-着色和b * -着色作为b-着色的改进变体

IF 1 3区数学

Discrete Applied Mathematics Pub Date : 2025-07-28 DOI: 10.1016/j.dam.2025.07.036

Manouchehr Zaker

引用次数: 0