A New Class of Polygonal Systems Representing Polycyclic Conjugated Hydrocarbons

Di-4-catafusenes are defined as catacondensed polygonal systems consisting of two tetragons each and otherwise only hexagons. Di- 4-catafusenes are enumerated by combinatorial constructions and by computer programming. For the unbranched systems (nonhelicenic + helicenic), as the main result of the present work, a complete mathematical solution is reported. A new algebraic approach has been employed, which involves a triangular matrix with some interesting mathematical properties

Unbranched Catacondensed Polygonal Systems Containing Hexagons and Tetragons

An algebraic solution for the isomer numbers of unbranched a-4- catafusenes is presented. An a-4-catafusene is a catacondensed polygonal system consisting of exactly o: tetragons each and otherwise only hexagons. This analysis, which makes use of certain triangular matrices including the Pascal triangle, is a continuation of a previous work on di-4-catafusenes. By serendipity, the problem was reversed in the sence that the systems were considered as possessing \u277 hexagons each and otherwise only tetragons. Under this viewpoint the enumeration problem could be solved more directly and led to explicit formulas. Finally, the resuIts are applied to catafusenes as a special case

Unbranched Catacondensed Polygonal Systems Containing Hexagons and Tetragons

An algebraic solution for the isomer numbers of unbranched a-4- catafusenes is presented. An a-4-catafusene is a catacondensed polygonal system consisting of exactly o: tetragons each and otherwise only hexagons. This analysis, which makes use of certain triangular matrices including the Pascal triangle, is a continuation of a previous work on di-4-catafusenes. By serendipity, the problem was reversed in the sence that the systems were considered as possessing \u277 hexagons each and otherwise only tetragons. Under this viewpoint the enumeration problem could be solved more directly and led to explicit formulas. Finally, the resuIts are applied to catafusenes as a special case

All-Benzenoid Systems: an Algebra of Invariants

The current invariants of all-benzenoids (h, n, m, nu na s - defined in the Introduction), in addition to the number of full and of empty hexagons (v and t), are studied. Their possible values are specified. Some of the relations between these invariants are summarized in a systematic way. The upper and lower bounds for all of them are accounted for as functions of any of these invariants

Benzenoid isomers with extremal values of the Kekulé structure count

454-457In families of benzenoid isomers, the molecules with maximum (minimum) Kekulé structure counts should possess maximum (minimum) stability and other distinguished properties. Identifying these extremal isomers turns out to be a difficult task. In this paper we solve such a problem for the class of isomers B(m,n), obtained from a benzenoid molecule B by attaching to its two fixed sites linear polyacene fragments of length m and n; m + n = constant

Enumeration of Polyhex Hydrocarbons to h: 17

This paper describes a rather efficient algorithm that enumerates nonisomorphic geometrically planar, simply connected polyhexes (hexagonal systems). It has been implemented in Modula-2 and used to determine andclassifythepertinentsystemswithli <lThexagons. Theresultforh:17,vi2., 1151594643, isnew