Strongly indexable graphs and applications

In 1990, Acharya and Hegde introduced the concept of strongly kk-indexable graphs: A (p,q)(p,q)-graph G=(V,E)G=(V,E) is said to be strongly  kk-indexable   if its vertices can be assigned distinct numbers 0,1,2,…,p−10,1,2,…,p−1 so that the values of the edges, obtained as the sums of the numbers assigned to their end vertices form an arithmetic progression k,k+1,k+2,…,k+(q−1)k,k+1,k+2,…,k+(q−1). When k=1k=1, a strongly kk-indexable graph is simply called a strongly indexable graph. In this paper, we report some results on strongly kk-indexable graphs and give an application of strongly kk-indexable graphs to plane geometry, viz; construction of polygons of same internal angles and sides of distinct lengths.