On combinatorial properties of Gruenberg-Kegel graphs of finite groups

被引：0
|
作者：
Chen, Mingzhu [1 ]
Gorshkov, Ilya [2 ,3 ]
Maslova, Natalia V. [4 ,5 ]
Yang, Nanying [6 ]
机构：
[1] Hainan Univ, Sch Math & Stat, Haikou 570225, Hainan, Peoples R China
[2] RAS, Sobolev Inst Math SB, Novosibirsk 630090, Russia
[3] Siberian Fed Univ, Krasnoyarsk 660041, Russia
[4] RAS, Krasovskii Inst Math & Mech UB, Ekaterinburg 620108, Russia
[5] Ural Fed Univ, Ekaterinburg 620002, Russia
[6] Jiangnan Univ, Sch Sci, Wuxi 214122, Peoples R China
来源：
MONATSHEFTE FUR MATHEMATIK | 2024年 / 205卷 / 04期
基金：
海南省自然科学基金; 俄罗斯科学基金会; 中国国家自然科学基金;
关键词：
Finite group; Centralizer of involution; Gruenberg-Kegel graph (prime graph); Strongly regular graph; Complete multipartite graph; PRIME GRAPH; RECOGNITION;
D O I：
10.1007/s00605-024-02005-6
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
If G is a finite group, then the spectrum omega(G) is the set of all element orders of G. The prime spectrum pi(G is the set of all primes belonging to omega(G). A simple graph Gamma(G) whose vertex set is pi(G) and in which two distinct vertices r and s are adjacent if and only if rs is an element of omega(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 Gamma(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.
引用
收藏
页码：711 / 723
页数：13
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