The even graceful labeling of a graph G with q edges means that there is an injection f : V(G) to { 0,1,1,1,2,...,2q+i/i= 1 to n} such that when each edge uv is assigned the label |f(u) – f(v)| the resulting edge labels are {1,3,5,...,2q-1}. A graph which admits an edge odd graceful labeling is called an edge-odd graceful graph. In this paper, the edge odd gracefulness of paths p1, p2, p3,..., ...

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-ev...

In 1991, Gnanajothi [4] proved that the path graph n P with n vertex and 1 n − edge is odd graceful, and the cycle graph m C with m vertex and m edges is odd graceful if and only if m even, she proved the cycle graph is not graceful if m odd. In this paper, firstly, we studied the graph m n C P ∪ when 4, 6,8,10 m = and then we proved that the graph m n C P ∪ is odd graceful if m is even. Finall...

A difference vertex labeling of a graph G is an assignment f of labels to the vertices of G that induces for each edge xy the weight |f(x)− f(y)| . A difference vertex labeling f of a graph G of size n is odd-graceful if f is an injection from V (G) to {0, 1, ..., 2n − 1} such that the induced weights are {1, 3, ..., 2n − 1}. We show here that any forest whose components are caterpillars is odd...

The ladder graph plays an important role in many applications as Electronics, Electrical and Wireless communication areas. The aim of this work is to present a new class of odd graceful labeling for the ladder graph. In particular, we show that the ladder graph Ln with m-pendant Ln mk1 is odd graceful. We also show that the subdivision of ladder graph Ln with m-pendant S(Ln)  mk1 is odd grace...

A shell graph is the join of a path P k of 'k' vertices and K 1. A subdivided shell graph can be constructed by subdividing the edges in the path of the shell graph. In this paper we prove that the disjoint union of two subdivided shell graphs is odd graceful and also one modulo three graceful. 1. Introduction A graph labeling is an assignment of integers to the vertices or edges, or both, subj...

Let G = (V, E) be a finite, simple and undirected graph having v = |V (G)| and e = |E(G)|. A graph G with q edges is said to be odd-graceful if there is an injection f : V (G) → {0, 1, 2, . . . , 2q−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 f...