Odd - Even Graceful Labeling for Different Paths using Padavon Sequence

Abstract

A function f is called an odd-even graceful labeling of a graph G if f: V(G) → {0,1,2,...,q} is injective and the induced function f : E(G) → { { 0,2,4,...,2q+2i/i= 1 to n} such that when each edge uv is assigned the label |f(u) – f(v)| the resulting edge labels are {2,4,6,...,2q}. A graph which admits an odd-even graceful labeling is called an odd-even graceful graph. In this paper, the odd-even gracefulness of paths p1, p2, p3,..., p11 is obtained.