EE-super vertex magic labelings of graphs

Let GG be a finite simple graph with pp vertices and qq edges. A vertex magic total labeling is a bijection from V(G)∪E(G)V(G)∪E(G) to the consecutive integers 1,2,3,…,p+q1,2,3,…,p+q with the property that for every u∈V(G)u∈V(G),f(u)+∑v∈N(u)f(uv)=kf(u)+∑v∈N(u)f(uv)=k for some constant kk. Such a labeling isEE-super if f(E(G))={1,2,3,…,q}f(E(G))={1,2,3,…,q}. A graph GG is called EE-super vertex magic if it admits a EE-super vertex magic labeling. In this paper, we study some basic properties of such labelings and we establish EE-super vertex magic labeling of some families of graphs. The main focus of this paper is on the EE-super vertex magicness of Hm,nHm,n and on some necessary conditions for a graph to be EE-super vertex magic.