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Integral Cayley Graphs over Finite Groups. / Konstantinova, Elena V.; Lytkina, Daria.

в: Algebra Colloquium, Том 27, № 1, 01.03.2020, стр. 131-136.

Результаты исследований: Научные публикации в периодических изданияхстатьяРецензирование

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Konstantinova EV, Lytkina D. Integral Cayley Graphs over Finite Groups. Algebra Colloquium. 2020 март 1;27(1):131-136. doi: 10.1142/S1005386720000115

Author

Konstantinova, Elena V. ; Lytkina, Daria. / Integral Cayley Graphs over Finite Groups. в: Algebra Colloquium. 2020 ; Том 27, № 1. стр. 131-136.

BibTeX

@article{d076c9b4dc0140188c97fb5d8893471f,
title = "Integral Cayley Graphs over Finite Groups",
abstract = "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}.",
keywords = "alternating group, Cayley graph, group algebra, Star graph, symmetric group",
author = "Konstantinova, {Elena V.} and Daria Lytkina",
note = "Publisher Copyright: {\textcopyright} 2020 Academy of Mathematics and Systems Science, Chinese Academy of Sciences. Copyright: Copyright 2020 Elsevier B.V., All rights reserved.",
year = "2020",
month = mar,
day = "1",
doi = "10.1142/S1005386720000115",
language = "English",
volume = "27",
pages = "131--136",
journal = "Algebra Colloquium",
issn = "1005-3867",
publisher = "World Scientific Publishing Co. Pte Ltd",
number = "1",

}

RIS

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 -

ID: 23665681