SOME RESULTS ON GRACEFUL CENTERS OF Pn AND RELATED α-GRACEFUL GRAPHS

SOME RESULTS ON GRACEFUL CENTERS OF Pn AND RELATED α-GRACEFUL GRAPHS

H. M. Makadia, V. J. Kaneria, P. Andharia, D. Jadeja

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Abstract

In this paper, we have proved that the graph obtained by joining two copies of a bipartite graceful graph by an edge with any two corresponding vertices of both the copies of graphs is  -graceful. We also proved path step tree and path double step tree are  -graceful and the graph Pm   Pn   P2 is  -graceful. Graceful center of graceful graph de ned. We also found some some graceful centers of path Pn. Acharya and Gill [1] proved Pn   Pm is  -graceful. In this paper we proved its generalized result.

Keywords

Graceful center of a graceful graph, universal graceful graph,  -graceful graph, Path step tree, Path double step tree.