The so-called leapfrog transformation that was first introduced for fullerenes (trivalent polyhedra with 12 pentagonal faces and all other faces hexagonal) is generalised to general polyhedra and maps on surfaces. All spherical polyhedra can be classified according to the i r leapfrog order. A polyhedron is said to be of Clar type if there exists a set of faces that cover each vertex exactly on...

We outline the construction of an algebraic (numerical) representation for Clar's valence formulas which in their geometrical form are illustrated with π-aromatic sextets as inscribed circles in benzenoid rings.

Benzene and pyrene can be synthetically linked to [o-COSAN]− keeping their aromaticity. In contrast, naphthalene anthracene are extruded in the same reaction. We have proven that extrusion is only favorable if number of Clar's π-sextets remains constant. Thus, Clar has answer whether an attached polycyclic aromatic hydrocarbon or not.

We introduce the notion of sink-stable sets of a digraph and prove a min-max formula for the maximum cardinality of the union of k sink-stable sets. The results imply a recent min-max theorem of Abeledo and Atkinson [1] on the Clar number of bipartite plane graphs and a sharpening of Minty’s coloring theorem [18]. We also exhibit a link to min-max results of Bessy and Thomassé [3] and of Sebő [...

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...

After 4 weeks of treatment, clarithromycin (CLAR) and amikacin showed similar antimicrobial activities against the Mycobacterium avium complex in mice. There was a difference, however, in the effectiveness of the drugs in different types of mice: both drugs displayed bactericidal effects in beige mice but only bacteriostatic effects in nude mice. Because the effectiveness of CLAR is less in nud...

The paper argues for the importance of utterances (as opposed to \sen-tences in context") as basic units in dialogue. The main case study is clar-iication: a characterization is provided within KOS, a recently developed synthesis of situation semantics and dialogue games, of the clariications that can follow up on an utterance. This involves outlining: (a) a theory of understanding for dialogue...