Arithmetic Sequential Graceful Labeling on Complete Bipartite Graph

Abstract

Consider the graph , which has  vertices and  edges and is simple, finite, connected, undirected, and non-trivial.  vertex set is V(G), while its edge set is  Let  be an injective function from  and for each edge  defined by  . Then the  is arithmetic sequential graceful labeling if  is bijective. The graph having arithmetic sequential graceful labeling is called arithmetic sequential graceful graph. This paper examined the arithmetic sequential graceful labeling for a few unique graphs.