保持w2属性的图运算

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

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引用次数: 0

摘要

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。

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Graph Operations Preserving W2-Property

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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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

期刊介绍： Electronic Notes in Discrete Mathematics is a venue for the rapid electronic publication of the proceedings of conferences, of lecture notes, monographs and other similar material for which quick publication is appropriate. Organizers of conferences whose proceedings appear in Electronic Notes in Discrete Mathematics, and authors of other material appearing as a volume in the series are allowed to make hard copies of the relevant volume for limited distribution. For example, conference proceedings may be distributed to participants at the meeting, and lecture notes can be distributed to those taking a course based on the material in the volume.