^{1}
Govindammal Aditanar College for Women Tiruchendur-628 215, Tamil Nadu, India
^{2}
Department of Mathematics, G.Venkataswamy Naidu College, Kovilpatti-628502,Tamilnadu,India.
Abstract
Let G be a (p,q) graph. An injective map f : E(G) → {±1,±2,...,±q} is said to be an edge pair sum labeling if the induced vertex function f^{*}: V (G) → Z - {0} defined by f^{*}(v) = Σ_{P∈Ev}f (e) is one-one where E_{v} denotes the set of edges in G that are incident with a vertex v and f^{*}(V (G)) is either of the form {±k_{1},±k_{2},...,±k_{p}_{/2}} or {±k_{1},±k_{2},...,±k_{(p-1)}_{/2}} U {±k_{(p+1)}_{/2}} according as p is even or odd. A graph with an edge pair sum labeling is called an edge pair sum graph. In this paper we prove that the graphs GL(n), double triangular snake D(T_{n}), W_{n}, Fl_{n}, <C_{m},K_{1,n}> and <C_{m} * K_{1,n}> admit edge pair sum labeling.