Summary of - Forbidden Values for Wiener Indices of Chain / Threshold Graphs

Document Type

Article

Abstract

Chain graphs and threshold graphs have received considerable attention of researchers in the field of spectral graph theory, due to extremity in the spectral radius among all the bipartite graphs (former one) and all the connected graphs (latter one). Wiener index of chain graphs have been studied in the literature and an algorithm returning a chain graph with the given Wiener index has been given. In this article, we give a list of integers which are forbidden values for Wiener indices of chain graphs, hence contributing further knowledge to the existing theory of inverse Wiener index problem. We further derive results on Wiener index of threshold graphs giving the bounds and carry out the similar study. We conclude the article with an algorithm for inverse Wiener index problem

for threshold graphs.

Index Terms: Chain, Bipartite graph, Bi-star graph, Wiener index.

Recommended Citation: K Arathi Bhat and Shahistha Hanif, Forbidden Values for Wiener Indices of Chain / Threshold Graphs, Engineering Letters, vol. 31, no. 1, pp180-185, 2023

Publication Date

2023

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