This paper addresses the problem of incorporating topological indices as structural descriptors for correlating properties in the design of product molecules with fine-tuned or optimized property values. Three different types of topological indices are considered: Randir's molecular connectivity indices, Kier's shape indices and the Wiener Index. The adjacency matrix representation which provid...

Convex hexagonal systems (CHS) i. e., hexagonal systems with no bay regions are studied. Among CHS with a fixed number of hexagons, the species with minimal/maximal number of inlets have minimal/maximal or maximal/minimal values for a variety of vertex–degree-based topological indices. These extremal CHS are characterized. 1 Convex hexagonal systems In this paper we study a special class of hex...

The secondary structure of RNAs can be represented by graphs at various resolutions. While it was shown that RNA secondary structures can be represented by coarse grain tree-graphs and meaningful topological indices can be used to distinguish between various structures, small RNAs are needed to be represented by full graphs. No meaningful topological index has yet been suggested for the analysi...

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.

Parasupersymmetric quantum mechanics is exploited to introduce a topological invariant associated with a pair of parameter dependent Fredholm (respectively elliptic diierential) operators satisfying two compatibility conditions. An explicit algebraic expression for this topological invariant is provided. The latter identiies the parasupersymmetric topological invariant with the sum of the analy...

Parasupersymmetric quantum mechanics is exploited to introduce a topological invariant associated with a pair of parameter dependent Fredholm (respectively elliptic differential) operators satisfying two compatibility conditions. An explicit algebraic expression for this topological invariant is provided. The latter identifies the parasupersymmetric topological invariant with the sum of the ana...