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.

The vertex set of the resonance graph of a hexagonal graph G consists of 1-factors of G, two 1-factors being adjacent whenever their symmetric difference forms the edge set of a hexagon of G. A decomposition theorem for the resonance graphs of catacondensed hexagonal graph is proved. The theorem intrinsically uses the Cartesian product of graphs. A canonical binary coding of 1-factors of cataco...

The Wiener Index, or the Wiener Number, also known as the “sum of distances” of a connected graph, is one of the quantities associated with a molecular graph that correlates nicely to physical and chemical properties, and has been studied in depth. An index proposed by Schultz is shown to be related to the Wiener Index for trees, and Ivan Gutman proposed a modification of the Schultz index with...

Various topological factors governing the electronic properties of infinitely large periodic polycyclic benzenoids are analyzed graph-theoretically by drawing the density of states (DS). The existence or non-existence of NBMO's in the hypothetical cyclic dimer of the network are shown to be crucial for the profile of DS. CATAHEXES AND PERIHEXES Owing to the rapid progress in organic synthesis t...

A benzenoid graph is a finite connected plane graph with no cut vertices in which every interior region is bounded by a regular hexagon of a side length one. A benzenoid graph G is elementary if every edge belongs to a 1-factor of G. A hexagon h of an elementary benzenoid graph is reducible, if the removal of boundary edges and vertices of h results in an elementary benzenoid graph. We characte...

The number of resonance structures (SC) for previously published concealed non-Kekuléan benzenoid hydrocarbons is determined. Using a simple computer program, analytical expressions for determining SC for various classes of non-Kekuléan (free-radical) benzenoid hydrocarbons are derived, and some properties of concealed non-Kekuléan benzenoid hydrocarbons are studied.

In this work we wish to report a method for computing the adjacency matrix of benzenoid hydrocarbons from their boundary codes. The carbon skeletons of benzenoids will be depicted by graphs, called benzenoid graphs• , which can be constructed in the plane by assembhng h regular hexagons in such a way that two hexagons have exactly one joint edge or are disjoint, and the covered area in the plan...

JERRY RAY DIAS. Can. J. Chem. 62, 2914 (1984). A new concept for isomer enumeration of peri-condensed benzenoid hydrocarbons (PAH6) based on the enumeration of their excised internal structures is presented. Formulas corresponding only to strictly peri-condensed benzenoid hydrocarbons can be identified from a previously derived Formula Periodic Table for PAH6. The number of benzenoid PAH6 isome...

The exact biosynthetic pathways leading to benzoic acid (BA) formation in plants are not known, but labeling experiments indicate the contribution of both beta-oxidative and non-beta-oxidative pathways. In Petunia hybrida BA is a key precursor for the production of volatile benzenoids by its flowers. Using functional genomics, we identified a 3-ketoacyl-CoA thiolase, PhKAT1, which is involved i...