Arithmetic Sequential Graceful Labeling of Complete Bipartite Graph with Pendant Edges

Let G be a simple, finite, connected, undirected, non-trivial graph with  vertices and  edges.  be the vertex set and  be the edge set of  Let  where a  and  is an injective function. If for each edge   defined by  is a bijective function then the function  is called arithmetic sequential graceful labeling. The graph with arithmetic sequential graceful labeling is called arithmetic sequential graceful graph. In this paper, we proved complete bipartite graph with pendant edges are arithmetic sequential graceful graph.