Some Results on the Generalized Cayley Graph of Complete Graphs

Suad Abdulaali Neamah; Ahmad Erfanian

doi:10.24996/ijs.2023.64.7.23

Authors

Suad Abdulaali Neamah Department of Pure Mathematics, Ferdowsi University of Mashhad, Mashhad, Iran
Ahmad Erfanian Department of Pure Mathematics and Center of Excellence in Analysis on Algebraic Structures‎, ‎Ferdowsi University of Mashhad‎, ‎Mashhad‎, ‎Iran https://orcid.org/0000-0002-9637-1417

DOI:

https://doi.org/10.24996/ijs.2023.64.7.23

Keywords:

Cayley graph, Complete graph, Generalized Cayley graph

Abstract

. Suppose that is the Cayley graph whose vertices are all elements of and two vertices and are adjacent if and only if . In this paper,we introduce the generalized Cayley graph denoted by which is a graph with a vertex set consisting of all column matrices in which all components are in and two vertices and are adjacent if and only if , where is a column matrix that each entry is the inverse of the similar entry of and is matrix with all entries in , is the transpose of and and m . We aim to provide some basic properties of the new graph and determine the structure of when is a complete graph for every , and n, m .