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...

A new parameter, related to and easily determined from the structure of a benzenoid system and that of a phenylene – the number of inlets (r) – is introduced. The connectivity (Randi}) index of both benzenoid systems and phenylenes is then shown to depend solely on the number of vertices and on r. A simple relation is established between the connectivity index of a phenylene and of the correspo...

In this note we present some new results on distances in benzenoids. An algorithm is presented which, for a given benzenoid system G bounded by a simple circuit 2 with n vertices, computes the Wiener index of G in O(n) time. Also we show that benzenoid systems have a convenient dismantling scheme, which can be derived by applying breadth-first search to their dual graphs. Our last result deals ...

The edge version of Szeged index and vertex version of PI index are defined very recently. They are similar to edge-PI and vertex-Szeged indices, respectively. The different versions of Szeged and PIindices are the most important topological indices defined in Chemistry. In this paper, we compute the edge-Szeged and vertex-PIindices of some important classes of benzenoid systems.

The local aromaticity of a series of benzenoid systems was determined through the use of structurally (HOMA) and magnetically (NICS) based measures, and also by using a new electronically based indicator of aromaticity, the para-delocalization index (PDI). The results were compared with the predictions of Clar’s aromatic -sextet rule. It is found that, for all analyzed benzenoid hydrocarbons ha...

We show that the molecular graph G of a benzenoid hydrocarbon admits an isometric embedding into the Cartesian product of three trees T1, T2, and T3 defined by three directions of the host hexagonal grid. Namely, to every vertex V of G one can associate an ordered triplet (V1, V2, V3) with Vi being a vertex of Ti (i ) 1, 2, 3), such that the graph-theoretic distance between two vertices u, V of...

It is shown that the vertices of benzenoid systems admit a labeling which reflects their distance relations. To every vertex of a molecular graph of a benzenoid hydrocarbon a sequence of zeros and ones (a binary number) can be associated, such that the number of positions in which these sequences differ is equal to the graph-theoretic vertex distance. It is shown by an example that such labelin...