Heptagonal Graceful Labeling of Star Related Graphs

Abstract

Numbers of the form (5n²-3n)/2 for all n ≥ 1 are called heptagonal numbers. Let G be a graph with p vertices and q edges. Let f:V(G)→{0,1,2,…,N_q } where N_q is the q^th heptagonal number be an injective function. Define the f*:E(G)→{1,7,18,…,N_q } such that f* (uv)=|f(u)-f(v)| for all edges uv∈E(G). If f*(E(G)) is a sequence of distinct consecutive numbers N₁,N₂,….,N_q then the function f is said to be heptagonal graceful labeling and the graph which admits such a labeling is called a heptagonal graceful graph. In this paper heptagonal graceful labeling of some graphs is studied.