Note on E-super vertex magic graphs

Abstract 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 vertex magic 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 ) + ∑ u v ∈ E ( G ) f ( u v ) = 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 E -super vertex magic if it admits an E -super vertex magic labeling. More recently Marimuthu and Balakrishnan (2012) studied some basic properties of such labeling and established E -super vertex magic labeling of some families of graphs. In this note we extend their results and more examples are also provided.