Vol. 11, No. 3, 2018

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On $G$-graphs of certain finite groups

Mohammad Reza Darafsheh and Safoora Madady Moghadam

Vol. 11 (2018), No. 3, 463–476

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 Γ(G,S). In this paper, we consider several types of groups G and study the existence of Hamiltonian and Eulerian paths and circuits in Γ(G,S).

$G$-graphs, finite group, Hamiltonian circuit, graphs, paths, circuits
Mathematical Subject Classification 2010
Primary: 05C25, 20F05
Secondary: 05C45
Received: 13 October 2016
Revised: 7 March 2017
Accepted: 18 July 2017
Published: 20 October 2017

Communicated by Kenneth S. Berenhaut
Mohammad Reza Darafsheh
School of Mathematics, Statistics and Computer Science, College of Science
University of Tehran
Safoora Madady Moghadam
School of Mathematics, Statistics and Computer Science
University of Tehran