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A class of planar well-covered graphs with girth four

✍ Scribed by Michael R. Pinter

Publisher
John Wiley and Sons
Year
1995
Tongue
English
Weight
616 KB
Volume
19
Category
Article
ISSN
0364-9024

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✦ Synopsis

Abstract

A well‐covered graph is a graph in which every maximal independent set is a maximum independent set; Plummer introduced the concept in a 1970 paper. The notion of a 1‐well‐covered graph was introduced by Staples in her 1975 dissertation: a well‐covered graph G is 1‐well‐covered if and only if G ‐ v is also well covered for every point v in G. Except for K~2~ and C~5~, every 1‐well‐covered graph contains triangles or 4‐cycles. We show that all planar 1‐well‐covered graphs of girth 4 belong to a specific infinite family, and we give a characterization of this family. © 1995 John Wiley & Sons, Inc.

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