Graph Operations Preserving W2-Property

Vadim E. Levit; Eugen Mandrescu

doi:10.1016/j.endm.2018.06.007

Graph Operations Preserving W₂-Property

Vadim E. Levit
, Eugen Mandrescu

Department of Mathematics

Research output: Contribution to journal › Article › peer-review

1 Scopus citations

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.

Original language	English
Pages (from-to)	35-40
Number of pages	6
Journal	Electronic Notes in Discrete Mathematics
Volume	68
DOIs	https://doi.org/10.1016/j.endm.2018.06.007
State	Published - Jul 2018

Keywords

class W
corona of graphs
graph join
independent set
rooted product of graphs
shedding vertex
well-covered graph

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10.1016/j.endm.2018.06.007

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title = "Graph Operations Preserving W2-Property",

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 Wn 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 Wn, using graphs from Wn or Wn+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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AB - A graph is well-covered if all its maximal independent sets are of the same size (Plummer, 1970). A graph G belongs to class Wn 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 Wn, using graphs from Wn or Wn+1. In this paper, we construct some more infinite subfamilies of the class W2 by means of corona, join, and rooted product of graphs.

KW - class W

KW - corona of graphs

KW - graph join

KW - independent set

KW - rooted product of graphs

KW - shedding vertex

KW - well-covered graph

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JO - Electronic Notes in Discrete Mathematics

JF - Electronic Notes in Discrete Mathematics

ER -

Graph Operations Preserving W₂-Property

Abstract

Keywords

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