Some Results on Path Related Even Sum Graphs

Abstract

Graph labeling is the allocation of integers to the vertex or edges or both subject to certain conditions. The concept of Even Sum Graphs was introduced by Chinju Krishna et al.. A graph G is called an even sum graph if there is a labeling η of its vertices with distinct non - negative even integers, so that for any two distinct vertices a and b; ab is an edge of G if and only if η(a) + η(b) = η(c) for some vertex c in G. The minimum number of isolated vertices required to make the graph G, an even sum graph is called the even sum number of G and is denoted by γ(G).