#### Vol. 11, No. 3, 2018

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On $G$-graphs of certain finite groups

Vol. 11 (2018), No. 3, 463–476
##### 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 $\Gamma \left(G,S\right)$.

##### Keywords
$G$-graphs, finite group, Hamiltonian circuit, graphs, paths, circuits
##### Mathematical Subject Classification 2010
Primary: 05C25, 20F05
Secondary: 05C45