In this paper the Clar covering polynomial of a hexagonal system is introduced. In fact it is a kind of F polynomial [4] of a graph, and can be calculated by recurrence relations. We show that the number of aromatic sextets (in a Clar formula), the number of Clar formulas, the number of Kekule structures and the first Herndon number for any Kekulean hexagonal system can be easily obtained by it...

An explicit combinatorial expression is obtained for the Zhang-Zhang polynomial (also known as “Clar cover polynomial”) of a large class of pericondensed benzenoid systems, the multiple linear hexagonal chains Mn,m. By means of this result, various problems encountered in the Clar theory of Mn,m are also resolved: counting of Clar and Kekulé structures, determining the Clar number, and calculat...

The Clar number of a (hydro)carbon molecule, introduced by Clar [E. Clar, The aromatic sextet, (1972).], is the maximum number of mutually disjoint resonant hexagons in the molecule. Calculating the Clar number can be formulated as an optimization problem on 2-connected planar graphs. Namely, it is the maximum number of mutually disjoint even faces a perfect matching can simultaneously alternat...

OBJECTIVE The clavulanic acid regulatory gene (claR) is in the clavulanic acid biosynthetic gene cluster that encodes ClaR. This protein is a putative regulator of the late steps of clavulanic acid biosynthesis. The aim of this research is the molecular cloning of claR, isolated from the Iranian strain of Streptomyces clavuligerus (S. clavuligerus). MATERIALS AND METHODS In this experimental ...

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...

The claR of Streptomyces clavuligerus in the clavulanic acid gene cluster encodes a transcriptional regulator that controls clavulanic acid biosynthesis. The main goal of this study was isolation and molecular detection of the claR gene and its cloning in the Streptomyces specific vector (pMA:: hyg). By cinsideration of the claR gene’s start codon, the specific primers were designed. After geno...

objective: the clavulanic acid regulatory gene (clar) is in the clavulanic acid biosynthetic gene cluster that encodes clar. this protein is a putative regulator of the late steps of clavulanic acid biosynthesis. the aim of this research is the molecular cloning of clar, isolated from the iranian strain of streptomyces clavuligerus (s. clavuligerus). materials and methods: in this experimental ...