On the Supermagic Edge-splitting Extension of Graphs

Abstract

A $(p,q)$-graph $G$ in which the edges are labeled $1,2,3,\dots ,q$ so that the vertex sums are constant, is called supermagic. If the vertex sum mod $p$ is a constant, then $G$ is called edge-magic. We investigate the supermagic characteristic of a simple graph $G$, and its edge-splitting extension $SPE(G,f)$. The construction provides an abundance of new supermagic multigraphs.