منابع مشابه
The Automorphism Group of Commuting Graph of a Finite Group
Let G be a finite group and X be a union of conjugacy classes of G. Define C(G,X) to be the graph with vertex set X and x, y ∈ X (x 6= y) joined by an edge whenever they commute. In the case that X = G, this graph is named commuting graph of G, denoted by ∆(G). The aim of this paper is to study the automorphism group of the commuting graph. It is proved that Aut(∆(G)) is abelian if and only if ...
متن کاملNon - commuting graph of a group ✩
Let G be a non-abelian group and let Z(G) be the center of G. Associate a graph ΓG (called noncommuting graph of G) with G as follows: Take G\Z(G) as the vertices of ΓG and join two distinct vertices x and y, whenever xy = yx. We want to explore how the graph theoretical properties of ΓG can effect on the group theoretical properties of G. We conjecture that if G and H are two non-abelian finit...
متن کاملcharacterization of the symmetric group by its non-commuting graph
the non-commuting graph $nabla(g)$ of a non-abelian group $g$ is defined as follows: its vertex set is $g-z(g)$ and two distinct vertices $x$ and $y$ are joined by an edge if and only if the commutator of $x$ and $y$ is not the identity. in this paper we 'll prove that if $g$ is a finite group with $nabla(g)congnabla(bs_{n})$, then $g cong bs_{n}$, where $bs_{n}$ is the symmetric group of degre...
متن کاملA Kind of Non-commuting Graph of Finite Groups
Let g be a fixed element of a finite group G. We introduce the g-noncommuting graph of G whose vertex set is whole elements of the group G and two vertices x,y are adjacent whenever [x,y] g and [y,x] g. We denote this graph by . In this paper, we present some graph theoretical properties of g-noncommuting graph. Specially, we investigate about its planarity and regularity, its clique number a...
متن کاملA note on the order graph of a group
The order graph of a group $G$, denoted by $Gamma^*(G)$, is a graph whose vertices are subgroups of $G$ and two distinct vertices $H$ and $K$ are adjacent if and only if $|H|big{|}|K|$ or $|K|big{|}|H|$. In this paper, we study the connectivity and diameter of this graph. Also we give a relation between the order graph and prime graph of a group.
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ژورنال
عنوان ژورنال: Bulletin of the London Mathematical Society
سال: 2013
ISSN: 0024-6093
DOI: 10.1112/blms/bdt005