Note on [formula omitted]-super vertex magic graphs

Abstract

Let G=(V(G),E(G)) be a finite simple graph with p=|V(G)| vertices and q=|E(G)| edges, without isolated vertices or isolated edges. A vertex magic total labeling is a bijection from V(G)∪E(G) to the consecutive integers 1,2,…,p+q, with the property that, for every vertex u in V(G), one has f(u)+∑uv∈E(G)f(uv)=k for some constant k. Such a labeling is called E-super vertex magic if f(E(G))={1,2,…,q}. A graph G is called E-super vertex magic if it admits an E-super vertex magic labeling. More recently Marimuthu and Balakrishnan (2012) studied some basic properties of such labeling and established E-super vertex magic labeling of some families of graphs. In this note we extend their results and more examples are also provided.