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 is E-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.
展开▼
