The generalized Cayley graph of complete graph K_n and complete multipartite graphs K_(n,n) and K_(n,n,n)

Ayat Abdulaali  Neamah; Abdulrahman H.  Majeed; Ahmad Erfanian

doi:10.24996/ijs.2022.63.7.31

Authors

Ayat Abdulaali Neamah Department of Mathematics, Al-Nahrain University, Baghdad, Iraq
Abdulrahman H. Majeed Department of Mathematics, University of Baghdad,Baghdad, Iraq
Ahmad Erfanian Department of Pure Mathematics, Ferdowsi University of Mashhad, Mashhad, Iran

DOI:

https://doi.org/10.24996/ijs.2022.63.7.31

Keywords:

Cayley graph, complete graph, bipartite graph, 3-partite graph, generalized Cayley graph, column matrix

Abstract

Suppose that is a finite group and is a non-empty subset of such that and . 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 that is a graph with vertex set consists of all column matrices 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 similar entry of and is matrix with all entries in , is the transpose of and . In this paper, we clarify some basic properties of the new graph and assign the structure of when is complete graph , complete bipartite graph and complete 3-partite graph for every .