Some results on the non-commuting graph of a finite group
نویسندگان
چکیده
منابع مشابه
some results on characterization of finite group by non commuting graph
the non commuting graph of a non-abelian finite 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 prove some new results about this graph. in particular we will give a new proof of theorem 3.24 of [2]. we also prove that if $g_1$, $g_2$, ..., $...
متن کاملSOME RESULTS ON THE COMPLEMENT OF THE INTERSECTION GRAPH OF SUBGROUPS OF A FINITE GROUP
Let G be a group. Recall that the intersection graph of subgroups of G is an undirected graph whose vertex set is the set of all nontrivial subgroups of G and distinct vertices H,K are joined by an edge in this graph if and only if the intersection of H and K is nontrivial. The aim of this article is to investigate the interplay between the group-theoretic properties of a finite group G and the...
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 کاملThe 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 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 کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: ScienceAsia
سال: 2019
ISSN: 1513-1874
DOI: 10.2306/scienceasia1513-1874.2019.45.482