An Algorithmic Approach to Compute the Metric Index of Chordal Ring Networks

Abstract

The metric is a non-negative assignment to the pairs of nodes in a connected network N, which assigns the number of links lying in a smallest path between the nodes in the pairs. A pair (a, b) of nodes in N is said to be uniquely identified by a node c of N if the metric assigned to the pair (a, c) is different from the metric assigned to the pair (b, c). The metric index of N is the minimum number of nodes in N chosen in such a manner that every two nodes in N are uniquely identified by a chosen node. It is said to be constant for a family of networks if it remains unchange with the extension in the networks. In this paper, we consider a family of chordal ring networks and propose an algorithm which assistances in proving, with the aid of mathematical induction and the concept of good nodes, that there is no change in the metric index of chordal ring networks with the extension in the networks.