On the Supermagic Edge-splitting Extension of Graphs

Abstract

A \((p,q)\)-graph \(G\) in which the edges are labeled \(1,2,3,\ldots,q\) 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.