On Co-Maximal Subgroup Graph of $Z_n$

Abstract

The co-maximal subgroup graph $Gamma(G)$ of a group $G$ is a graph whose vertices are non-trivial proper subgroups of $G$ and two vertices $H$ and $K$ are adjacent if $HK = G$. In this paper, we study and characterize various properties like diameter, domination number, perfectness, hamiltonicity, etc. of $Gamma(mathbb{Z}_n)$.