Some results on graceful centers of Pn and related α-graceful graphs

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 α-graceful. We also proved path step tree and path double step tree are α-graceful and the graph Pm × Pn × P2 is α-graceful. Graceful center of graceful graph defined. We also found some some graceful centers of path Pn. Acharya and Gill [1] proved Pn × Pm is α-graceful. In this paper we proved its generalized result.Publisher's Versio