Distance properties of molecular graphs form an important topic in chemical graph theory.1 To justify this statement just recall the famous Wiener index which is also known as the Wiener number. This index is the first2 but also one of the most important topological indices of chemical graphs. Its research is still very active; see recent reviews3,4 and several new results in a volume5 dedicate...

We predict the number of hexagonal systems consisting of 24 and 25 hexagons to be H 24 = 122237774262384 and H 25 = 606259305418149, with 6 and 5 signiicant digits, respectively. Further estimates for H n up to n = 31 are also given. Informally speaking, a hexagonal system can be viewed as a connected arrangement of hexagonal cells packed in the same way as the typical honeycomb arrangement in ...

We predict the number of hexagonal systems consisting of and hexagons to be H and H with and signi cant digits respectively Further estimates for Hn up to n are also given Hexagonal Systems Informally speaking a hexagonal system can be viewed as a connected arrangement of hexagonal cells packed in the same way as the typical honeycomb arrangement in a bee hive More formally it is a nite connect...

The algebraic Kekulé structure of a finite catacondensed benzenoid graph with h hexagons is described by a binary code of length h. The procedure can be reversed, any (algebraic) Kekulé structure can be recovered from its binary code. c © 2007 Elsevier Ltd. All rights reserved.

This report briefly describes the development and applications of net-sign graph theory. The current work enunciates the graph (molecule) signature of nonalternant non-benzenoid hydrocarbons with odd member of rings (non-bipartite molecular graphs) based on chemical signed graph theory. Experimental evidences and Hückel spectrum reveal that structure possessing nonbonding molecular orbital (NBM...

It is shown that the number of Clar formulas of a Kekuléan benzenoid system B is equal to the number of subgraphs of the resonance graph of B isomorphic to the Cl(B)-dimensional hypercube, where Cl(B) is the Clar number of B.

Zagreb indices belong to better known and better researched topological indices. We investigate here their ability to discriminate among benzenoid graphs and arrive at some quite unexpected conclusions. Along the way we establish tight (and sometimes sharp) lower and upper bounds on various classes of benzenoids.

An irregularity index IR(Γ) of a graph Γ is nonnegative numeric quantity (i.e., IR(Γ)≥0) such that IR(Γ)=0 iff regular graph. In this paper, we show IRC closely correlates with the normal boiling point Tbp and standard heat formation ΔHfo lower benzenoid hydrocarbons. The correlation models fit data efficiently for both are linear. We develop further mathematical properties by calculating its e...

A topological descriptor is regarded as a numerical parameter derived by using mathematical tools from the molecular graph of different chemical structures. The theory paramount section chemistry. In this section, there are many parameters, that have very useful characteristics to study structure chemicals. article, we investigate indices concealed non-kekulean benzenoid hydrocarbon graph. We w...