Upper bounds on the energy of graphs in terms of matching number

IF 16.4 1区化学 Q1 CHEMISTRY, MULTIDISCIPLINARY

Accounts of Chemical Research Pub Date : 2021-01-01 DOI:10.2298/aadm201227016a

S. Akbari, Abdullah J. Alazemi, Milica Andjelic

引用次数: 4

Abstract

The energy of a graph G, ?(G), is the sum of absolute values of the eigenvalues of its adjacency matrix. The matching number ?(G) is the number of edges in a maximum matching. In this paper, for a connected graph G of order n with largest vertex degree ? ? 6 we present two new upper bounds for the energy of a graph: ?(G) ? (n-1)?? and ?(G) ? 2?(G)??. The latter one improves recently obtained bound ?(G) ? {2?(G)?2?e + 1, if ?e is even; ?(G)(? a + 2?a + ?a-2?a), otherwise, where ?e stands for the largest edge degree and a = 2(?e + 1). We also present a short proof of this result and several open problems.

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用匹配数表示图的能量上界

图G的能量?(G)是它的邻接矩阵的特征值的绝对值之和。匹配数?(G)是最大匹配中的边数。对于顶点度最大的连通图G (n阶)？我们提出了图能量的两个新的上界:?(G) ?(n - 1) ? ?(G) ?2 (G) ? ?。后者改进了最近得到的界?(G) ?{2 (G) ? 2 ?E + 1，如果E是偶数;(G) ?A + 2?A + A -2 A)，否则，其中?e表示最大边度，A = 2(?我们也给出了这个结果的一个简短证明和几个开放问题。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Accounts of Chemical Research 化学-化学综合

CiteScore

31.40

自引率

1.10%

发文量

312

审稿时长

2 months

期刊介绍： Accounts of Chemical Research presents short, concise and critical articles offering easy-to-read overviews of basic research and applications in all areas of chemistry and biochemistry. These short reviews focus on research from the author’s own laboratory and are designed to teach the reader about a research project. In addition, Accounts of Chemical Research publishes commentaries that give an informed opinion on a current research problem. Special Issues online are devoted to a single topic of unusual activity and significance. Accounts of Chemical Research replaces the traditional article abstract with an article "Conspectus." These entries synopsize the research affording the reader a closer look at the content and significance of an article. Through this provision of a more detailed description of the article contents, the Conspectus enhances the article's discoverability by search engines and the exposure for the research.