Note on E-super vertex magic graphs

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 vertexmagic 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 Esuper vertexmagic if it admits an E-super vertexmagic labeling. More recentlyMarimuthu and Balakrishnan (2012) studied some basic properties of such labeling and established Esuper vertex magic labeling of some families of graphs. In this note we extend their results and more examples are also provided. © 2014 Elsevier B.V. All rights reserved.