Wiener Index and Degree Distance Generalizations on Basic Graphs

Year 2025, Volume: 8 Issue: 2, 83 - 94, 26.12.2025

Mehmet Ümit Gürsoy

https://doi.org/10.70030/sjmakeu.1803647

Abstract

Graph theory is a branch of science founded in the 18th century by the renowned mathematician Leonhard Euler, who solved the 'Seven Bridges of Königsberg' problem. Over time, graph theory has been used to solve problems in various scientific fields, introducing many new concepts into this domain. Many measurements have been defined for various purposes in graph theory. Some of these measurements are indices which have been defined for various tasks. Wiener index and degree distance are two of them. It is known that the Wiener index of a molecular graph correlates with certain physical and chemical properties of a molecule. Both indices are based on the concept of distance. In this article, the results of the Wiener and degree distance indices on the basic graph types (path, star, circle, wheel, complete, and complete bipartite graphs) are presented using inductive and deductive methods. Furthermore, the minimum and maximum values, as well as the bounds of these indices, are established. These definitions introduce a new approach to indices that have long been studied and widely applied.

Keywords

Wiener index , degree distance , vulnerability , graph indices

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