Integral Cayley Graphs over Finite Groups

Standard

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

In: Algebra Colloquium, Vol. 27, No. 1, 01.03.2020, p. 131-136.

Research output: Contribution to journal › Article › peer-review

Harvard

Konstantinova, EV & Lytkina, D 2020, 'Integral Cayley Graphs over Finite Groups', Algebra Colloquium, vol. 27, no. 1, pp. 131-136. https://doi.org/10.1142/S1005386720000115

APA

Konstantinova, E. V., & Lytkina, D. (2020). Integral Cayley Graphs over Finite Groups. Algebra Colloquium, 27(1), 131-136. https://doi.org/10.1142/S1005386720000115

Vancouver

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

Author

Konstantinova, Elena V. ; Lytkina, Daria. / Integral Cayley Graphs over Finite Groups. In: Algebra Colloquium. 2020 ; Vol. 27, No. 1. pp. 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",

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

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