Graph Operations Preserving W2-Property

Q2 Mathematics

Electronic Notes in Discrete Mathematics Pub Date : 2018-07-01 DOI:10.1016/j.endm.2018.06.007

Vadim E. Levit, Eugen Mandrescu

引用次数: 0

Abstract

A graph is well-covered if all its maximal independent sets are of the same size (Plummer, 1970). A graph G belongs to class W_n if every n pairwise disjoint independent sets in G are included in n pairwise disjoint maximum independent sets (Staples, 1975). Clearly, W₁ is the family of all well-covered graphs. Staples showed a number of ways to build graphs in W_n, using graphs from W_n or W_n+1. In this paper, we construct some more infinite subfamilies of the class W₂ by means of corona, join, and rooted product of graphs.

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保持w2属性的图运算

如果一个图的所有最大独立集的大小相同，那么这个图就是覆盖良好的(Plummer, 1970)。如果图G中的每n个对不相交独立集都包含在n个对不相交最大独立集中，则图G属于类Wn (Staples, 1975)。显然，W1是所有覆盖良好的图的族。斯台普斯展示了几种在Wn中构建图形的方法，使用Wn或Wn+1中的图形。本文利用图的电晕、连接和根积构造了W2类的几个无限子族。

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

Electronic Notes in Discrete Mathematics Mathematics-Discrete Mathematics and Combinatorics

CiteScore

1.30

自引率

0.00%

发文量

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