On the Clique Numbers of Non-commuting Graphs of Certain Groups

被引：12

作者：

Abdollahi, A. ^{[1
,2
]}

Azad, A. ^{[1
]}

Hassanabadi, A. Mohammadi ^{[1
,3
]}

Zarrin, M. ^{[1
]}

机构：

[1] Univ Isfahan, Dept Math, Esfahan 8174673441, Iran

[2] Inst Res Fundamental Sci IPM, Sch Math, Tehran, Iran

[3] Shaikhbahaee Univ, Esfahan 8179735296, Iran

来源：

ALGEBRA COLLOQUIUM | 2010年 / 17卷 / 04期

关键词：

pairwise non-commuting elements of a group; non-commuting graph; clique number of a graph; PAIRWISE NONCOMMUTING ELEMENTS; FINITE-GROUPS; ABELIAN SUBGROUPS; MAXIMAL SUBSETS; MINIMAL COVERS; SN;

D O I：

10.1142/S1005386710000581

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

Let G be a non-abelian group. The non-commuting graph A(G) of G is defined as the graph whose vertex set is the non-central elements of G and two vertices are joint if and only if they do not commute. In a finite simple graph Gamma, the maximum size of complete subgraphs of Gamma is called the clique number of Gamma and denoted by omega(Gamma). In this paper, we characterize all non-solvable groups G with omega(A(G)) <= 57 where 57 is the clique number of the non-commuting graph of the projective special linear group PSL(2,7). We also determine omega(A(G)) for all finite minimal simple groups G.

引用

页码：611 / 620

页数：10

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