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