• Φ – GRACEFUL LABELING OF SOME CLASS OF GRAPHS

Abstract

G=(p, q) be a graph with p vertices and q edges. The Φ – graceful labeling of a graph G with ‘m’ vertices and ‘n’ edges is an injective function f : V (G) → {0, 1, 2,……n-1} such that the induced function f* : E(G) → N is given by f* (uv) = 2{f (u) + f(v)}, the resulting edge labels are distinct. In this paper all graphs are finite, without loops and multiple edges. We prove results on Φ – graceful labeling of binary tree, crown graph and cycle with one chord.