One Point Union of $\alpha-$graceful Graphs

Abstract

The notation of $\alpha$-labeling of a graph is the natural generalization of graceful labeling and it helps produce new graceful graphs by some graph operations. In this paper, we have proved that one point union of two $\alpha$-graceful graphs is $\alpha$-graceful under some conditions, one point union of an $\alpha$-graceful graph and a graceful graph is graceful. We have also proved that the consecutive one point union of a finite number of $\alpha$-graceful graphs with a graceful graph by merging one vertex under some conditions is also a graceful graph. These results help enlarge the class of graceful graphs.