Klaus Szymanski

Molecular topological index

The molecular topological index (MTI) has been systematically tested for counterexamples (two or more nonisomorphic structures with the same MTI number). The analysis was carried out for alkane trees with up to 16 atoms. The search for counterexamples was positive : the first pair of alkane trees with identical MTI numbers was found in the octane family. The more disturbing finding was that two nonisomorphic alkane trees of different sizes may also possess the same MTI value. An attempt to redefine the MTI in terms of only the distance matrix and the valency matrix was abortive

On the concept of the weighted spanning tree of dualist

The concepts of dual, inner dual and dualist are reviewed. The application of these concepts to polyhexes is briefly described. The concepts of a spanning tree and a weighted spanning tree of dualist are introduced. The uses of the weighted spanning tree of dualist in coding and enumerating polyhex hydrocarbons are outlined.

Use of small computers for large computations: Enumerations of polyhex hydrocarbons

The enumeration of polyhex hydrocarbons with up to 16 hexagons is reported. These results are now for the first time available

On irreducible endospectral graphs

The paper considers endospectral trees, a special class of graphs associated with the production of numerous isospectral graphs. Endospectral graphs have been considered in the literature sporadically (the name was suggested very recently [M. Randic, SIAM J. Algebraic Discrete Meth. 6, 145 (1985)]). They are characterized by the presence of a pair of special vertices that, if replaced by any fragment, produce an isospectral pair of graphs. Recently Jiang [Y. Jiang, Sci. Sin. 27, 236 (1984)] and Randic and Kleiner (M. Randic and A. F. Kleiner, ‘‘On the construction of endospectral trees,’’ submitted to Ann. NY Acad. Sci.) considered alternative constructive approaches to endospectral trees and listed numerous such graphs. The listing of all such trees having n=16 or fewer vertices has been undertaken here. It has been found that relatively few endospectral trees have novel structural features and cannot be reduced to some already known endospectral tree. These few have been named ‘‘irreducible endospectral...

Computer generation of all 1-factors for a class of graphs with all vertices of degree two or three

Abstract An algorithm is proposed for the enumeration and display of all 1-factors for a class of graphs with all vertices of degree two or three.

Computer enumeration of substituted polyhexes

Abstract A computer-assisted combinatorial method for enumerating substituted polyhexes (benzenoid hydrocarbons) is presented. Because of the symmetry among isomer counts the numerical values are given only for the first half of each series of isomers. The other half of results can be obtained by means of the simple rule. The size of polyhexes considered is up to 10 hexagons.

On the determinant of the adjacency-plus-distance matrix as the topolgical index for characterizing alkanes

The determinant of the adjacency-plus-distance matrix has been systematically tested for examples that would disprove a supposition that it is a unique topological index (TI) for alkanes. The analysis was carried out for alkane trees with up to 20 sites. The search was fruitful: The first pair of alkane trees with identical TI numbers was already found in the nonane family

Enumeration and classification of coronoid hydrocarbons: note to a note

Abstract A double coronoid is a polyhex with two holes. Altogether 161 such systems with up to 15 hexagons have been generated and enumerated with the use of a computer. The systems are classified into Kekulean (normal and essentially disconnected) and non-Kekulean, and catacondensed (including primitive ) and Pericondensed. The distribution into symmetry groups is specified. The forms of all the generated systems are displayed, and the Kekule structure counts are given.

The walk ID number revisited. [Erratum to document cited in CA118:146918]

ERRATA The Walk ID Number Revisited [ J . Chem. Znf. Comput. Sci. 33,23 1-233 (1993)J By Wolfgang R. Muller, Klaus Szymanski, Jan V. b o p , Zlatko MihaliC, and Nenad TrinajstiC*. The Computer Centre, The Heinrich Heine University, D-40225 Dusseldorf, The Federal Republic of Germany, Faculty of Science and Mathematics, The University of Zagreb, HR-41001 Zagreb, The Republic of Croatia, and The Rugjer BolkoviE Institute, HR-41001 Zagreb, The Republic of Croatia

On the number of square-cell configurations

SummaryThe numbers of simply and multiply connected square-cell configurations are computed. The computation is based on the original algorithm for constructive enumeration of animals which is founded on the DAST (dualist angle-restricted spanning tree) code.