边能化学图和12阶边能图的分类

IF 1 3区数学 Q3 MATHEMATICS, APPLIED

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":"边能化学图和12阶边能图的分类","authors":"Péter Csikvári , Ivan Damnjanović , Marko Milošević , Ivan Stanković , Dragan Stevanović","doi":"10.1016/j.dam.2025.07.035","DOIUrl":null,"url":null,"abstract":"<div><div>The energy <span><math><mrow><mi>E</mi><mrow><mo>(</mo><mi>G</mi><mo>)</mo></mrow></mrow></math></span> of a simple graph <span><math><mi>G</mi></math></span> is the sum of absolute values of the eigenvalues of its adjacency matrix. A borderenergetic graph of order <span><math><mrow><mi>n</mi><mo>∈</mo><mi>N</mi></mrow></math></span> is any noncomplete graph <span><math><mi>G</mi></math></span> such that <span><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></span>. 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":1.0000,"publicationDate":"2025-07-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"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\":null,\"url\":null,\"abstract\":\"<div><div>The energy <span><math><mrow><mi>E</mi><mrow><mo>(</mo><mi>G</mi><mo>)</mo></mrow></mrow></math></span> of a simple graph <span><math><mi>G</mi></math></span> is the sum of absolute values of the eigenvalues of its adjacency matrix. A borderenergetic graph of order <span><math><mrow><mi>n</mi><mo>∈</mo><mi>N</mi></mrow></math></span> is any noncomplete graph <span><math><mi>G</mi></math></span> such that <span><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></span>. 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\":1.0000,\"publicationDate\":\"2025-07-31\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Discrete Applied Mathematics\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://www.sciencedirect.com/science/article/pii/S0166218X25004251\",\"RegionNum\":3,\"RegionCategory\":\"数学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q3\",\"JCRName\":\"MATHEMATICS, APPLIED\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Discrete Applied Mathematics","FirstCategoryId":"100","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S0166218X25004251","RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"MATHEMATICS, APPLIED","Score":null,"Total":0}

引用次数: 0

摘要

简单图G的能量E(G)是其邻接矩阵特征值的绝对值之和。n∈n阶的边能图是任意满足E(G)=E(Kn)=2n−2的非完全图G。在这里，我们将两阶段计算机辅助搜索与理论论证结合起来，表明只有三个边界能化学图，从而完成了Li等人（2017）的早期发现。我们执行了两阶段的计算机辅助搜索，也找到了所有566个12阶的边界能图，从而纠正和扩展了Furtula和Gutman（2017）先前搜索的结果。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

查看原文本刊更多论文

Classification of borderenergetic chemical graphs and borderenergetic graphs of order 12

The energy

E (G)

of a simple graph

G

is the sum of absolute values of the eigenvalues of its adjacency matrix. A borderenergetic graph of order

n \in N

is any noncomplete graph

G

such that

E (G) = E (K_{n}) = 2 n - 2

. 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).

求助全文

通过发布文献求助，成功后即可免费获取论文全文。去求助

来源期刊

Discrete Applied Mathematics 数学-应用数学

CiteScore

2.30

自引率

9.10%

发文量

422

审稿时长

4.5 months

期刊介绍： The aim of Discrete Applied Mathematics is to bring together research papers in different areas of algorithmic and applicable discrete mathematics as well as applications of combinatorial mathematics to informatics and various areas of science and technology. Contributions presented to the journal can be research papers, short notes, surveys, and possibly research problems. The "Communications" section will be devoted to the fastest possible publication of recent research results that are checked and recommended for publication by a member of the Editorial Board. The journal will also publish a limited number of book announcements as well as proceedings of conferences. These proceedings will be fully refereed and adhere to the normal standards of the journal. Potential authors are advised to view the journal and the open calls-for-papers of special issues before submitting their manuscripts. Only high-quality, original work that is within the scope of the journal or the targeted special issue will be considered.