On the Conjecture Related to the Energy of Graphs with Self–Loops

IF 2.9 2区 化学 Q2 CHEMISTRY, MULTIDISCIPLINARY
Irena M. Jovanović, E. Zogic, E. Glogic
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引用次数: 2

Abstract

Let Gσ be a graph obtained by attaching a self-loop, or just a loop, for short, at each of σ chosen vertices of a given graph G. Gutman et al. have recently introduced the concept of the energy of graphs with self-loops, and conjectured that the energy E(G) of a graph G of order n is always strictly less than the energy E(Gσ) of a corresponding graph Gσ, for 1 ≤ σ ≤ n − 1. In this paper, a simple set of graphs which disproves this conjecture is exposed, together with some remarks regarding the standard deviations of the (adjacency) eigenvalues of G and Gσ, respectively.
关于自环图能量的猜想
设Gσ为在给定图G的σ个选定顶点上附加一个自环或简称为一个环而得到的图G。Gutman等人最近引入了自环图能量的概念,并推测n阶图G的能量E(G)总是严格小于对应图Gσ的能量E(Gσ),当1≤σ≤n−1时。本文给出了一组简单的图来反驳这个猜想,并给出了G和Gσ的(邻接)特征值的标准差。
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
CiteScore
4.40
自引率
26.90%
发文量
71
审稿时长
2 months
期刊介绍: MATCH Communications in Mathematical and in Computer Chemistry publishes papers of original research as well as reviews on chemically important mathematical results and non-routine applications of mathematical techniques to chemical problems. A paper acceptable for publication must contain non-trivial mathematics or communicate non-routine computer-based procedures AND have a clear connection to chemistry. Papers are published without any processing or publication charge.
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