Some Edge Pair Sum Graphs

Abstract

An injective map f : E(G)→{± 1,±2, … ,±q} is said to be an edge pair sum labeling of a graph G(p, q) if the induced vertex function f* : V(G)→Z − {0} defined by f* (v)=∑e∈Evf(e) is one – one, where Ev denotes the set of edges in G that are incident with a vertex v and f*(V(G)) is either of the form or according as p is even or odd. A graph which admits edge pair sum labeling is called an edge pair sum graph. In this paper we prove that the one point union of cycles, the perfect binary tree, shadow graph, total graph and Pn2 admit edge pair sum labeling.