In this paper, Kekule structures of benzenoid chains are considered. It has been shown that the coefficients of a B_n (x) Morgan-Voyce polynomial equal to the number of k-matchings (m(G,k)) of a path graph which has N=2n+1 points. Furtermore, two relations are obtained between regularly zig-zag nonbranched catacondensed benzenid chains and Morgan-Voyce polynomials and between regularly zig-zag ...

Hexagonal chains are a special class of catacondensed benzenoid system and phenylene polycyclic aromatic compounds. Recently, A family Sombor indices was introduced by Gutman in the chemical graph theory. It had been examined that these may be successfully applied on modeling thermodynamic properties In this paper, we study expected values random hexagonal chains, consider some graphs such as g...

K e y w o r d s P l a n e graph, Outerplane graph, Bipartite graph, Perfect matching, Z-transformation graph. 1. I N T R O D U C T I O N A graph G is a planar graph if it can be embedded in plane such that edges only intersect at their end vertices. A plane graph is such an embedding. A plane graph is called an outerplane graph if all vertices are lie on the boundary of the exterior face. A gra...

Let G be a planar embedded 2-connected graph. Then the vertices of its resonance graph R(G) are the 1-factors of G, two 1-factors being adjacent whenever their symmetric difference is a bounded face of G. For a class of graphs containing the chemically important catacondensed benzenoid graphs we show that the resonance graphs are median. In particular, if G belongs to this class, R(G) has an is...

a recently published paper [t. došlić, this journal 3 (2012) 25-34] considers the zagrebindices of benzenoid systems, and points out their low discriminativity. we show thatanalogous results hold for a variety of vertex-degree-based molecular structure descriptorsthat are being studied in contemporary mathematical chemistry. we also show that theseresults are straightforwardly obtained by using...

Fibonacenes (zig-zag unbranched catacondensed benzenoid hydrocarbons) are a class of polycyclic conjugated systems whose molecular graphs possess remarkable properties, often related with the Fibonacci numbers. This article is a review of the chemical graph theory of fibonacenes, with emphasis on their Kekulé–structure–related and Clar–structure–related properties. ————————————————— ∗Supported ...