Algorithm for finding the Wiener indices of some families of graphs

Abstract

In this paper we provide algorithms for finding the Wiener indices of SM family of Graphs and Hanoi Graphs. The Hanoi Graph is related to the popular Tower of Hanoi puzzle. SM family of Graphs consists of SM sum graphs, SM balancing graphs, its complement graphs and its subgraphs. The SM sum graph is associated with the relationship between the powers of 2 and positive integers. The SM balancing graphs are formed by using the fact that all positive integers can be written as a linear combination of powers of 3. These are systematically arranged graphs. Also the topological indices like Wiener indices are more important in life science and computer science. The values of Wiener indices need to be calculated for different values of n. A normal ordinary method will be difficult for large values of n. So we are deriving algorithmic method to find the Wiener indices and then the roots of the HOSOYA polynomial in the cases of these graphs.