On Super Edge-Magic Strength and Deficiency of Graphs

A graph G is called super edge-magic if there exists a one-to-one mapping f from V (G ) *** E (G ) onto {1, 2, 3, *** , |V (G )| + |E (G )|} such that for each uv *** E (G ), f (u ) + f (uv ) + f (v ) = c (f ) is constant and all vertices of G receive all smallest labels. Such a mapping is called super edge-magic labeling of G . The super edge-magic strength of a graph G is defined as the minimum of all c (f ) where the minimum runs over all super edge-magic labelings of G . Since not all graphs are super edge-magic, we define, the super edge-magic deficiency of a graph G as either minimum n such that G *** nK 1 is a super edge-magic graph or + *** if there is no such n . In this paper, the bound of super edge-magic strength and the super edge-magic deficiency of some families of graphs are obtained.