Cayley graphs of finite groups
type: Item
instance of: scholarly article
title: Cayley graphs of finite groups
zbMATH Open document ID: 0665.20018
DOI: 10.1016/0021-8693(88)90033-6
author: Paul-Herrmann Zieschang
published in: Journal of Algebra
publication date: 1988-01-01T00:00:00Z
review text: Cayley graphs \(\Gamma\) (G,T) of a finite group G defined by normal generating sets T (unions of conjugacy classes) are studied via irreducible complex characters. The author obtains a formula equating the eigenvalues of the Cayley graph to weighted sums of the character values at points over T. As a consequence, he provides a formula to compute the number of paths of length n connecting 1 to any vertex in G. Under the assumption that G possesses a cyclic subgroup of odd order, this number is an invariant for elements of the same order. The number is also invariant for adjacent elements of the Cayley graph under more restrictive conditions and a particular choice of generating set T.
Mathematics Subject Classification ID: 20F05
Mathematics Subject Classification ID: 20C15
Mathematics Subject Classification ID: 05C25
Mathematics Subject Classification ID: 20C05
zbMATH DE Number: 4087914
zbMATH Keywords: Cayley graphs
zbMATH Keywords: finite group
zbMATH Keywords: normal generating sets
zbMATH Keywords: irreducible complex characters
MaRDI profile type: Publication
full work available at URL: 0021-8693(88)90033-6
OpenAlex ID: W2037125231
cites work: Solvability of groups of odd order
cites work: Q5577154
cites work: Q4103728
cites work: Some uses of class algebra constants
description: scientific article; zbMATH DE number 4087914