Clar's aromatic sextet theory provides a good means to describe the aromaticity of benzenoid hydrocarbons, which was mainly based on experimental observations. Clar defined sextet pattern and Clar number of benzenoid hydrocarbons, and he observed that for isomeric benzenoid hydrocarbons, when Clar number increases the absorption bands shift to shorter wavelength, and the stability of these isom...

a fullerene graph is a 3−connected planar graph whose faces are pentagons and hexagons.the clar number of a fullerene is the maximum size of sextet patterns, the sets of disjointhexagons which are all m-alternating for a kekulé structure m of f. an exact formula of clarnumber of some fullerene graphs and a class of carbon nanocones are obtained in this paper.

SU(3) gauge theory with overlap fermions in the 2-index symmetric (sextet) and fundamentalrepresentations is considered. A priori it is not known what the pattern of chiral symmetry breakingis in a higher dimensional representation although the general expectation is that if two representationsare both complex, the breaking pattern will be the same. This expectation is verified for ...

While briefly reviewing how the concepts of strictly pericondensed, strain-free, Clar's aromatic sextet, and symmetry are interconnected in the topological correspondence between strictly pericondensed and total resonant sextet (TRS) benzenoid hydrocarbons, new structural correlations in isomer numbers, symmetry distributions, and empty rings between various strain-free TRS benzenoids made up o...

A number of mathematical relations for the sextet polynomial are derived. A graph has been introduced (the so called C-graph), representing those properties of a benzenoid system which are essential in the sextet theory of Clar. The main structural properties of the C-graph are determined. The obtained results contribute towards a better understanding of the algebraic and combinatorial backgrou...

A fullerene graph is a cubic 3-connected plane graph with (exactly 12) pentagonal faces and hexagonal faces. Let Fn be a fullerene graph with n vertices. A set H of mutually disjoint hexagons of Fn is a sextet pattern if Fn has a perfect matching which alternates on and off each hexagon in H. The maximum cardinality of sextet patterns of Fn is the Clar number of Fn. It was shown that the Clar n...

The relationships between inner dual, dualist, sextet dualist, and antisextet dualist graphs and excised internal structures are fully delineated. It is proven that the antisextet dualist graph uniquely characterizes all strain-free benzenoids. At the same time, it is shown that the excised internal structure and dualist graph of the retro-leapfrog of all strain-free total resonant sextet benze...

Electroweak symmetry breaking can be a consequence of color sextet quark chiral symmetry breaking, with sextet pions producing the longitudinal components of the electroweak vector bosons. If so, a special solution of QCD is involved, for which the high-energy S-Matrix can be constructed “semiperturbatively” via the chiral anomaly and reggeon diagrams. An infra-red fixed point and the starting ...

SU(3) gauge theory in the 2-index symmetric (sextet) and fundamental representations is considered in symmetric and periodic boxes. Using the overlap formulation in the quenched approximation it is shown that the topological charge obtained from the sextet index theorem always leads to an integer value and agrees with the charge obtained from the fundamental index theorem in the continuum. At l...

A fullerene graph is a cubic 3-connected plane graph with (exactly 12) pentagonal faces and hexagonal faces. Let Fn be a fullerene graph with n vertices. A set H of mutually disjoint hexagons of Fn is a sextet pattern if Fn has a perfect matching which alternates on and off each hexagon in H. The maximum cardinality of sextet patterns of Fn is the Clar number of Fn. It was shown that the Clar n...