Mathematica, Volume (64 (87)), No (2), Year (2022-12) , Pages (247-254)

Title : ( On a generalized Cayley graph of column matrices of elements of a finite group )

Authors: AYAT ABDULAALI NEAMAH , Ahmad Erfanian , ABDULRAHMAN H. MAJEED ,

Citation: BibTeX | EndNote

Abstract

Let G be a finite group and let Xm be an m × 1 column matrix of elements of G. Let S be a nonempty subset of G such that e / ∈ S and S−1 ⊆ S. If Cay(G, S) is the usual Cayley graph, whose vertices are all elements of G and two vertices x and y are adjacent if and only if xy−1 ∈ S, then the generalized Cayley graph Caym(G, S) is a graph with vertex set consisting of all column matrices Xm, and two vertices Xm and Ym are adjacent if and only if Xm[(Ym)−1]t ∈ M(S), where Ym−1 is a column matrix that each entry is the inverse of the corresponding entry of Ym, M(S) is an m×m matrix with all entries in S, [Y −1]t is the transpose of Y −1, and m ≥ 1. It is obvious that if m = 1, then Caym(G, S) and Cay(G, S) coincide. In this article, we establish some basic properties of the new graph and determine the structure of Caym(G, S) when Cay(G, S) is a cycle, Cn, for every n ≥ 3.

Keywords

, Cayley graph, cycle graph, generalized Cayley graph, column matrix.
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@article{paperid:1094160,
author = {AYAT ABDULAALI NEAMAH and Erfanian, Ahmad and ABDULRAHMAN H. MAJEED},
title = {On a generalized Cayley graph of column matrices of elements of a finite group},
journal = {Mathematica},
year = {2022},
volume = {64 (87)},
number = {2},
month = {December},
issn = {1222-9016},
pages = {247--254},
numpages = {7},
keywords = {Cayley graph; cycle graph; generalized Cayley graph; column matrix.},
}

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%0 Journal Article
%T On a generalized Cayley graph of column matrices of elements of a finite group
%A AYAT ABDULAALI NEAMAH
%A Erfanian, Ahmad
%A ABDULRAHMAN H. MAJEED
%J Mathematica
%@ 1222-9016
%D 2022

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