On Weakly Indexable Graphs

By : S.M. Hegde, P. Shankaran

Page No: 173-209

Abstract
A (p,q)-graph G is said to be strongly k-indexable, if its vertices can be assigned distinct nonnegative integers 0, 1, 2..., p?1 so that the values of the edges, obtained as the sum of the numbers assigned to their end vertices, can be arranged as an arithmetic progression k, k+1, k + 2,..., k + (q?1). In this paper we introduce and study weakly indexable graphs. A graph G is said to be weakly k-indexable, if its vertices can be assigned distinct non-negative integers 0, 1, 2,...,p?1 so that the values of the edges, obtained as the sum of the numbers assigned to their end vertices form the multiset of numbers k, k +1, k +2,..., k + t, where t is a positive integer less than q?1. In this paper, we obtain some necessary conditions on weakly k-indexable graphs and investigate classes of graphs which admit weak indexer.

Authors :
S.M. Hegde : Dept. of Mathematical and Computational Sciences, N.I.T.K., Surathkal, Srinivasanagar-575025, India. 
P. Shankaran : N.M.A.M. Institute of Technology, Nitte-574110, India