On $G$-graphs of certain finite groups

Abstract

The notion of $G$-graph was introduced by Bretto et al. and has interesting properties. This graph is related to a group $G$ and a set of generators $S$ of $G$ and is denoted by $\Gamma \left(G,S\right)$. In this paper, we consider several types of groups $G$ and study the existence of Hamiltonian and Eulerian paths and circuits in $\Gamma \left(G,S\right)$.