Graceful labeling on torch graph

Graceful Tree Labeling

Graceful and odd graceful labeling of some graphs

In this paper, we prove that the square graph of bistar Bn,n, the splitting graph of Bn,n and the splitting graph of star K1,n are graceful graphs. We also prove that the splitting graph and the shadow graph of bistar Bn,n admit odd graceful labeling.

Odd Graceful Labeling of Acyclic Graphs

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, . . . , 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} and f is called an odd graceful labeling of G. Motivated by the work of Z. Gao [6] in which he studied th...

On Odd Graceful Labeling of the Generalization of Cyclic Snakes

The objective of this paper is to present a new class of odd graceful graphs. In particular, we show that the linear cyclic snakes (1, k) C4snake and (2, k) C4snake are odd graceful. We prove that the linear cyclic snakes (1, k) C6snake and (2, k) C6snake are odd graceful. We also prove that the linear cyclic snakes (1, k) C8snake and (2, k) C8snake are odd graceful. We generalize the above res...

Improper Graceful and Odd-graceful Labellings of Graph Theory

Abstract In this paper we define some new labellings for trees, called the in-improper and out-improper odd-graceful labellings such that some trees labelled with the new labellings can induce graceful graphs having at least a cycle. We, next, apply the new labellings to construct large scale of graphs having improper graceful/odd-graceful labellings or having graceful/odd-graceful labellings.