On benzenoid systems with minimal number of inlets

On benzenoid systems with a minimal number of inlets

Recent experimental methods have made it possible to synthesize very large benzenoid molecules, sometimes referred to as “graphenes”.1–3 These have found unprecedented applications as organic materials for electronic and optoelectronic devices.2,3 As large benzenoid systems have countless possible isomers,4–6 it is a task of theoretical chemistry to help indicate those species that may possess ...

On the Clar Number of Benzenoid Graphs

A Clar set of a benzenoid graph B is a maximum set of independent alternating hexagons over all perfect matchings of B. The Clar number of B, denoted by Cl(B), is the number of hexagons in a Clar set for B. In this paper, we first prove some results on the independence number of subcubic trees to study the Clar number of catacondensed benzenoid graphs. As the main result of the paper we prove a...

On General Sum-Connectivity Index of Benzenoid Systems and Phenylenes

On Distances in Benzenoid Systems

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...

Minimal solution of fuzzy linear systems

In this paper, we use parametric form of fuzzy number and we converta fuzzy linear system to two linear system in crisp case. Conditions for the existence of a minimal solution to $mtimes n$ fuzzy linear equation systems are derived and a numerical procedure for calculating the minimal solution is designed. Numerical examples are presented to illustrate the proposed method.