TY - JOUR

T1 - Integral Cayley Graphs over Finite Groups

AU - Konstantinova, Elena V.

AU - Lytkina, Daria

N1 - Publisher Copyright: © 2020 Academy of Mathematics and Systems Science, Chinese Academy of Sciences. Copyright: Copyright 2020 Elsevier B.V., All rights reserved.

PY - 2020/3/1

Y1 - 2020/3/1

N2 - We prove that the spectrum of a Cayley graph over a finite group with a normal generating set S containing with every its element s all generators of the cyclic group is integral. In particular, a Cayley graph of a 2-group generated by a normal set of involutions is integral. We prove that a Cayley graph over the symmetric group of degree n no less than 2 generated by all transpositions is integral. We find the spectrum of a Cayley graph over the alternating group of degree n no less than 4 with a generating set of 3-cycles of the form (k i j) with fixed k, as {-n+1, 1-n+1, 22 -n+1, ..., (n-1)2 -n+1}.

AB - We prove that the spectrum of a Cayley graph over a finite group with a normal generating set S containing with every its element s all generators of the cyclic group is integral. In particular, a Cayley graph of a 2-group generated by a normal set of involutions is integral. We prove that a Cayley graph over the symmetric group of degree n no less than 2 generated by all transpositions is integral. We find the spectrum of a Cayley graph over the alternating group of degree n no less than 4 with a generating set of 3-cycles of the form (k i j) with fixed k, as {-n+1, 1-n+1, 22 -n+1, ..., (n-1)2 -n+1}.

KW - alternating group

KW - Cayley graph

KW - group algebra

KW - Star graph

KW - symmetric group

UR - http://www.scopus.com/inward/record.url?scp=85080111186&partnerID=8YFLogxK

U2 - 10.1142/S1005386720000115

DO - 10.1142/S1005386720000115

M3 - Article

AN - SCOPUS:85080111186

VL - 27

SP - 131

EP - 136

JO - Algebra Colloquium

JF - Algebra Colloquium

SN - 1005-3867

IS - 1

ER -