Some Graceful and $\alpha$-Graceful Labeling for Cycle Related Graphs

V. J. Kaneria1, Payal Akbari1 and Nishaba Parmar1


1Department of Mathematics, Saurashtra University, Rajkot, Gujarat, India.

Abstract: In this paper we present graceful and $\alpha $-graceful labeling for some cycle related graphs. We have proved that the graph obtained by adding two pendent vertices at distance two and one chord between them in a cycle $C_n$ and the graph obtained by adding arbitrary pendent vertices at two different places at distance two in a cycle $C_n$, when $n$ is odd are graceful graphs, while the graph obtained by adding alternate pendent vertices in a cycle $C_n$, when $n$ is even and the graph obtained by adding arbitrary pendent vertices at two different places at distance two in a cycle $C_n$, when $n$ is even are $\alpha $-graceful graphs.
Keywords: Labeling, Graceful Labeling, $\alpha$-Graceful Labeling, Cycle Related Graphs.


Cite this article as: V. J. Kaneria, Payal Akbari and Nishaba Parmar, Some Graceful and $\alpha$-Graceful Labeling for Cycle Related Graphs, Int. J. Math. And Appl., vol. 9, no. 4, 2021, pp. 65-73.

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