Heptagonal Graceful Labeling on Simple Graphs

Abstract

Heptagonal numbers are numbers that have the form  for all .Consider the graph G with p vertices and q edges. Assume that  is an injective function with being the  heptagonal number. Define  such that  for all edges .If  is a sequence of distinct sequential numbers  then the function  is said to have heptagonal graceful labeling and the graph admitting such a labeling is termed as heptagonal graceful graph. This work investigates heptagonal graceful labeling of various graphs.