• STRUCTURE GRACEFUL INDEX OF COMPLETE GRAPHS

Abstract

A graceful labeling of a graph G with q edges and vertex set V is an injection f: V(G) →{0,1,2,….,q} with the property that the resulting edge labels are also distinct, where an edge incident with vertices u and v is assigned the label |f(u)-f(v)|.  A graph which admits a graceful labeling is called a graceful graph.  In this paper we define the structure graceful index of complete graphs.  Also we prove that the structure graceful index of complete graph K_n is 2 for 4 < n < 11.  We extend this result to determine the structure graceful index of complete graphs for greater values of n.