Polygonal Graceful Labeling of Some Simple Graphs

Abstract

Let  be a graph with vertices and edges.  Let andbe the vertex set and edge set of respectively.  A polygonal graceful labeling of a graph  is an injective function , where  is a set of all non-negative integers that induces a bijection , where  is the  polygonal number such that for every edge .  A graph which admits such labeling is called a polygonal graceful graph. For , the above labeling gives triangular graceful labeling. For , the above labeling gives tetragonal graceful labeling and so on. In this paper, polygonal graceful labeling is introduced and polygonal graceful labeling of some simple graphs is studied