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

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 .

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Published

2022-07-31

Issue

Section

Mathematics

How to Cite

The generalized Cayley graph of complete graph K_n and complete multipartite graphs K_(n,n) and K_(n,n,n). (2022). Iraqi Journal of Science, 63(7), 3103-3110. https://doi.org/10.24996/ijs.2022.63.7.31

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