On a Construction of Supermagic Graphs

Abstract

Given two graphs $G$ and $H$, the composition of $G$ with $H$ is the graph with vertex set $V(G)\times V(H)$ in which $(u_1,v_1)$ is adjacent to $(u_2,v_2)$ if and only if $u_1{u}_2\in E(G)$ or $u_1=u_2$ and $v_1{v}_2\in E(H)$. In this paper, we prove that the composition of a regular supermagic graph with a null graph is supermagic. With the help of this result, we show that the composition of a cycle with a null graph is always supermagic.