The order supergraph of the power graph of a finite group

Authors : Asma HAMZEH, Ali Reza ASHRAFI

Pages : 1978-1989

View : 9 | Download : 8

Publication Date : 0000-00-00

Article Type : Research Paper

Abstract :The power graph $\mathcal{P}insert ignore into journalissuearticles values(G);$ is a graph with group elements as a vertex set and two elements are adjacent if one is a power of the other. The order supergraph $\mathcal{S}insert ignore into journalissuearticles values(G);$ of the power graph $\mathcal{P}insert ignore into journalissuearticles values(G);$ is a graph with vertex set $G$ in which two elements $x, y \in G$ are joined if $oinsert ignore into journalissuearticles values(x); | oinsert ignore into journalissuearticles values(y);$ or $oinsert ignore into journalissuearticles values(y); | oinsert ignore into journalissuearticles values(x);$. The purpose of this paper is to study certain properties of this new graph together with the relationship between $\mathcal{P}insert ignore into journalissuearticles values(G);$ and $\mathcal{S}insert ignore into journalissuearticles values(G);$.
Keywords : Power graph, order supergraph, proper order supergraph