On odd-graceful labeling of disjoint union of graphs

Abstract

Let G = (V, E) be a finite, simple and undirected graph. A graph G with q edges is said to be odd-graceful if there is an injection f: V(G) → {0,1,2,...,2c - 1} such that, when each edge xy is assigned the label|f(x) - f(y)|, the resulting edge labels are {1,3,5,..., 2q - 1}. Motivated by the work of Z. Gao [6], we have defined odd graceful labeling for some other union of graphs. In this paper we formulate odd-graceful labeling for disjoint unions of graphs consisting of generalized combs, ladders, stars, bistars, caterpillars and paths.