An explicit, non-recursive formula for the Wiener index of any given benzenoid chain is derived, greatly speeding up calculations and rendering it manually manageable, through a novel envisioning of chains as ternary strings. Previous results are encompassed and two completely new and useful ones are obtained, a formula to determine Wiener indices of benzenoid chains in periodic patterns, and a...

The Padmakar-Ivan (PI) index is a Wiener-Szeged-like topological index, which reflects certain structural features of organic molecules. In this paper, we study the maximum PI indices and the minimum PI indices for trees and unicyclic graphs respectively.

A graph is maximal k-degenerate if each induced subgraph has a vertex of degree at most k and adding any new edge to the violates this condition. In paper, we provide sharp lower upper bounds on Wiener indices graphs order $$n \ge 1$$ . chordal every cycle in triangle k$$ are k-trees. For k-trees 2k+2$$ , characterize all extremal for bound.

the padmakar-ivan (pi) index is a first-generation topological index (ti) based on sums overall edges between numbers of edges closer to one endpoint and numbers of edges closer to theother endpoint. edges at equal distances from the two endpoints are ignored. an analogousdefinition is valid for the wiener index w, with the difference that sums are replaced byproducts. a few other tis are discu...

Inequalities provide a way to study topological indices relatively. There are two major classes of topological indices: degree-based and distance-based indices. In this paper we provide a relative study of these classes and derive inequalities between degree-based indices such as Randić connectivity, GA, ABC, and harmonic indices and distance-based indices such as eccentric connectivity, connec...

The Wiener index is a graph invariant that has found extensive application in chemistry. In addition to that a generating function, which was called the Wiener polynomial, who’s derivate is a q-analog of the Wiener index was defined. In an article, Sagan, Yeh and Zhang in [The Wiener Polynomial of a graph, Int. J. Quantun Chem., 60 (1996), 959969] attained what graph operations do to the Wiene...