STAR SUPER EDGE MAGIC DEFICIENCY OF GRAPHS

Abstract

A graph G is called edge - magic if there is a bijec- tive function f : V (G)∪E(G) → {1, 2, . . . , |V (G)|+|E(G)|} such that for every edge xy ∈ E(G), f(x) + f(xy) + f(y) = c is a con- stant, called the valence of f. A graph G is said to be super edge - magic if f(V (G)) = {1, 2, . . . , |V (G)|}. Let G be a graph with p vertices with V (G) = {v1, v2, . . . , vp}. In G, every vertex vi is identified to the center vertex of Smi , for some mi ≥ 0, 1 ≤ i ≤ n, where S0 = K1 and the graph is denoted by G(m1,m2,...,mp). Let M(G) = {(m1,m2, . . . ,mp)|G(m1,m2,...,mp) is a super edge magic graph }. The star super edge magic deficiency Sμ∗(G) is defined as Sμ∗(G) = min(m1,,m2,...,mp)(m1 + m2 + · · · + mp) if M(G) 6= ∅; +∞ if M(G) = ∅. In this paper we determine the star super edge magic deficiency of certain classes of graphs.