Odd gracefulness of the chain of trim kites and star graph

Abstract

Gnanajothi (Gnanajothi, R.B. (1991). Topics in Graph Theory, Ph.D. Thesis, Madurai Kamaraj University, Tamil Nadu, India) defined a graph $G$ with $q$ edges to be odd graceful if there is an one-one function $f$ from $V\left(G\right)$ to $\left\{0,1,2,\ldots ,\left(2q-1\right)\right\}$ such that, when each edge $xy$ is assigned the label $\left|f\left(x\right)-f\left(y\right)\right|$, the resulting edge labels are $\left\{1,3,\ldots ,\left(2q-1\right)\right\}$. A graph which reveals an odd graceful labeling is called an odd graceful graph. In this paper, we prove that the graphs of chain of Trim kite and Star graph are odd graceful.