منابع مشابه
groups for which the noncommuting graph is a split graph
the noncommuting graph $nabla (g)$ of a group $g$ is asimple graph whose vertex set is the set of noncentral elements of$g$ and the edges of which are the ones connecting twononcommuting elements. we determine here, up to isomorphism, thestructure of any finite nonabeilan group $g$ whose noncommutinggraph is a split graph, that is, a graph whose vertex set can bepartitioned into two sets such t...
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.
متن کاملOn the planarity of a graph related to the join of subgroups of a finite group
Let $G$ be a finite group which is not a cyclic $p$-group, $p$ a prime number. We define an undirected simple graph $Delta(G)$ whose vertices are the proper subgroups of $G$, which are not contained in the Frattini subgroup of $G$ and two vertices $H$ and $K$ are joined by an edge if and only if $G=langle H , Krangle$. In this paper we classify finite groups with planar graph. ...
متن کاملthe coprime graph of a group
the coprime graph $gg$ with a finite group $g$ as follows: take $g$ as the vertex set of $gg$ and join two distinct vertices $u$ and $v$ if $(|u|,|v|)=1$. in the paper, we explore how the graph theoretical properties of $gg$ can effect on the group theoretical properties of $g$.
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...
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ژورنال
عنوان ژورنال: Boletim da Sociedade Paranaense de Matemática
سال: 2016
ISSN: 2175-1188,0037-8712
DOI: 10.5269/bspm.v34i1.23517