Strongly indexable graphs and applications

In 1990, Acharya and Hegde introduced the concept of strongly k -indexable graphs: A ( p , q ) -graph G = ( V , E ) is said to be strongly k -indexable if its vertices can be assigned distinct numbers 0 , 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 ) . When k = 1 , a strongly k -indexable graph is simply called a strongly indexable graph. In this paper, we report some results on strongly k -indexable graphs and give an application of strongly k -indexable graphs to plane geometry, viz; construction of polygons of same internal angles and sides of distinct lengths.