On combinatorial properties of Gruenberg–Kegel graphs of finite groups

On combinatorial properties of Gruenberg–Kegel graphs of finite groups Full article

Journal

Monatshefte fur Mathematik
ISSN: 0026-9255 , E-ISSN: 1436-5081

Output data

Year: 2024, Volume: 205, Pages: 711–723 Pages count : 13 DOI: 10.1007/s00605-024-02005-6

Tags

Finite group · Centralizer of involution · Gruenberg–Kegel graph (prime graph) · Strongly regular graph · Complete multipartite graph

Authors

Chen Mingzhu ¹ , Gorshkov Ilya ^2,3 , Maslova Natalia V. ^4,5 , Yang Nanying ⁶

Affiliations

1	School of Mathematics and Statistics, Hainan University, Haikou, 570225, Hainan, People's Republic of China
2	Sobolev Institute of Mathematics SB RAS, Novosibirsk, Russia, 630090
3	Siberian Federal University
4	Krasovskii Institute of Mathematics and Mechanics UB RAS, Yekaterinburg, Russia, 620108
5	Ural Federal University
6	School of Science, Jiangnan University, Wuxi, 214122, People's Republic of China

Funding (2)

1	Russian Science Foundation	24-41-10004
2	Министерство науки и высшего образования РФ	075-02-2024-1428

If G is a finite group, then the spectrum ω(G) is the set of all element orders of G. The prime spectrum π(G) is the set of all primes belonging to ω(G). A simple graph (G) whose vertex set is π(G) and in which two distinct vertices r and s are adjacent if and only if rs ∈ ω(G) is called the Gruenberg–Kegel graph or the prime graph of G. In this paper, we prove that if G is a group of even order, then the set of vertices which are non-adjacent to 2 in (G) forms a union of cliques. Moreover, we decide when a strongly regular graph is isomorphic to the Gruenberg–Kegel graph of a finite group.

Chen M. , Gorshkov I. , Maslova N.V. , Yang N.
On combinatorial properties of Gruenberg–Kegel graphs of finite groups
Monatshefte fur Mathematik. 2024. V.205. P.711–723. DOI: 10.1007/s00605-024-02005-6 WOS Scopus РИНЦ OpenAlex

Submitted:	Jan 28, 2024
Accepted:	Jul 18, 2024
Published print:	Aug 20, 2024
Published online:	Aug 20, 2024

Web of science:	WOS:001294983600001
Scopus:	2-s2.0-85201640280
Elibrary:	73467091
OpenAlex:	W4401766542

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