The Average Size of Independent Sets in Unicyclic Graphs

IF 0.4 4区数学 Q4 MATHEMATICS

Contributions To Discrete Mathematics Pub Date : 2022-11-23 DOI:10.47443/cm.2022.051

Zuwen Luo, Kexiang Xu, A. Cevik, I. Gutman

引用次数: 0

Abstract

The average size of independent sets of a graph ( avi ) is considered. It can be viewed as the logarithmic derivative of the independence polynomial at 1 . Lower and upper bounds on avi for unicyclic graphs of a given order are determined, and the respective extremal graphs are given. The unicyclic graphs that maximize (minimize) avi coincide with those that maximize (minimize, respectively) the number of independent sets.

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单环图中独立集的平均大小

考虑图的独立集的平均大小(avi)。它可以看作是独立多项式在1处的对数导数。确定了给定阶数的单环图的avi的下界和上界，并给出了相应的极值图。最大化(最小化)avi的单环图与最大化(分别最小化)独立集数量的单环图重合。

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

Contributions To Discrete Mathematics MATHEMATICS-

CiteScore

1.30

自引率

0.00%

发文量

期刊介绍： Contributions to Discrete Mathematics (ISSN 1715-0868) is a refereed e-journal dedicated to publishing significant results in a number of areas of pure and applied mathematics. Based at the University of Calgary, Canada, CDM is free for both readers and authors, edited and published online and will be mirrored at the European Mathematical Information Service and the National Library of Canada.