Product Order Relatively Prime Graph of a Group

Abstract

In this paper we introduce the concept of a product order relatively prime graph (Simply called PORP graph) $\Gamma_{porp}(G)$ of a finite group $G$. The product order relatively prime graph $\Gamma_{porp}(G)$ is a graph with $V(\Gamma_{porp}(G))=G$ and two vertices $a$ and $b$ are adjacent in $\Gamma_{porp}(G)$ if either $(o(a),o(ab))=1$ or $(o(b),o(ab))=1$. Also we obtain certain graph parameters such as clique number, chromatic number, independent number and domination number.