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.

References
1. F. Harary, Graph theory, Addition Wesley, Massachusetts, (1972).
2. A. Rosa, On certain valuation of graph, Theory of Graphs (Rome, July 1966), Goden and Breach, N. Y. and Paris, (1967), 349-355.
3. S. W. Golomb, How to number a graph, Graph Theory and Computing (R. C. Read. Ed.) Academic Press, New York, (1972), 23-37.
4. J. A. Gallian, A Dynamic Survey of Graph Labeling, The Electronics Journal of Combinatorics, 22(2020), \#DS6.
5. V. J. Kaneria and H. M. Makadia, Some graceful graphs, J. of Math. Res., 4(1)(2012), 54-57.
6. V. J. Kaneria, H. M. Makadia and M. M. Jariya, Graceful labeling for cycle of graphs, Int. J. of Math. Res., 6(2)(2014), 173-178.

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