Formula omitted]-super vertex magic labelings of graphs

Abstract

Let G be a finite simple graph with p vertices and q edges. A vertex magic total labeling is a bijection from V(G)∪E(G) to the consecutive integers 1,2,3,…,p+q with the property that for every u∈V(G),f(u)+∑v∈N(u)f(uv)=k for some constant k. Such a labeling isE-super if f(E(G))={1,2,3,…,q}. A graph G is called E-super vertex magic if it admits a E-super vertex magic labeling. In this paper, we study some basic properties of such labelings and we establish E-super vertex magic labeling of some families of graphs. The main focus of this paper is on the E-super vertex magicness of Hm,n and on some necessary conditions for a graph to be E-super vertex magic.