On the two-sided group digraph with a normal adjacency matrix

Document Type : Full Length Article

Authors

1 Mathematics, Basic Faculty, Shahid Rajaee Teacher Training University

2 Department of Mathematics, Faculty of Science, Shahid Rajaee Teacher Training University

Abstract

This article explores the adjacency matrix of a two-sided group graph and
its properties. We introduce the two-sided color group digraph to generalize the Cayley color graph and the two-sided group digraph. We also
obtain the adjacency matrix of the latter digraph and provide a criterion for
determining the normality of the adjacency matrix of a two-sided group graph.
Moreover, we prove that if all the two-sided group digraphs of valency two for
a certain group G are normal, then G is a Hamiltonian group. We also show
that if a strongly connected two-sided group digraph of valency two is normal,
the corresponding group is isomorphic to the product of two groups: a cyclic
group with either Tk,n or Hp,q, or an abelian group.

Graphical Abstract

On the two-sided group digraph with a normal adjacency matrix

Keywords

Main Subjects


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Volume 9, Issue 2
June 2024
Pages 103-111
  • Receive Date: 01 April 2024
  • Revise Date: 15 April 2024
  • Accept Date: 17 May 2024
  • Publish Date: 01 June 2024