Strongly indexable graphs and applications

Abstract

In 1990, Acharya and Hegde introduced the concept of strongly k-indexable graphs: A (p, q)-graph G = (V, E) is said to be stronglyk -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. 2009 Elsevier B.V. All rights reserved.