The Well-Covered Dimension of Products of Graphs

Abstract

We discuss how to find the well-covered dimension of a graph that is the Cartesian product of paths, cycles, complete graphs, and other simple graphs. Also, a bound for the well-covered dimension of $K_n\times G$ is found, provided that $G$ has a largest greedy independent decomposition of length $c<n$. Formulae to find the well-covered dimension of graphs obtained by vertex blowups on a known graph, and to the lexicographic product of two known graphs are also given.