Commun. Korean Math. Soc. 2020; 35(2): 359-370
Online first article January 3, 2020 Printed April 30, 2020
https://doi.org/10.4134/CKMS.c190071
Copyright © The Korean Mathematical Society.
Baha' Abughazaleh, Omar Abughneim, Hasan Al-Ezeh
The University of Jordan; The University of Jordan; The University of Jordan
A graph $G$ is called a well covered graph if every maximal independent set in $G$ is maximum, and co-well covered graph if its complement is a well covered graph. We study some properties of a co-well covered graph and we characterize when the join, the corona product, and cartesian product are co-well covered graphs. Also we characterize when powers of trees and cycles are co-well covered graphs. The line graph of a graph which is co-well covered is also studied.
Keywords: Well covered graphs, co-well covered graphs, cliques
MSC numbers: 05C69 and 05C75
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