TY - JOUR
TI - The generalized Cayley graph of complete graph K_n and complete multipartite graphs K_(n,n) and K_(n,n,n)
PY - 2022/07/31
Y2 - 2024/06/19
JF - Iraqi Journal of Science
JA - Iraqi Journal of Science
VL - 63
IS - 7
SE - Mathematics
DO - 10.24996/ijs.2022.63.7.31
UR - https://doi.org/10.24996/ijs.2022.63.7.31
SP - 3103-3110
AB - 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 .
ER -