Pendant and isolated vertices of comaximal graphs of modules

Abstract

A comaximal graph Γ(M) is an undirected graph with vertex set as the collection of all submodules of a module M and any two vertices A and B are adjacent if and only if A + B = M. We discuss characteristics of pendant vertices in Γ(M). We also observe features of isolated vertices in a special spanning subgraph in Γ(M).