A comparative analysis of ten topological indices is made. No index is found to discriminate isomers uniquely. A combined topological index, named the superindex, consisting of a number of topological indices is proposed. Information theory is applied to express all components of the superindex on a common quantitative scale. The superindex is tested on the sample of 427 graphs consisting of all acyclic, monocyclic, and bicyclic graphs with 4–8 vertices.
AbstractsThe sum of the topological distances in the molecular graph (the Wiener number) is used for a topological characterization of the condensed polycyclic molecular systems. This topological index discriminates well the isomeric cyclic molecules. In addition, it also properly reflects their structural features. On this basis the principal points of molecular cyclicity are formulated in 15 rules.La somme des distances topologiques dans un graphe molkculaire (le nombre de Wiener) est utilisee pour caracttriser topologiquement les systemes molkculaires polycycliques condenses. Cet index topologique distingue tres bien les molecules cycliques isomeriques. En outre il reflete aussi leur proprietes structurales correctement. Avec les notions ainsi elaborees les points principaux de la cyclicite moltculaire sont formules en 15 regles.Die Summe der topologischen Abstande in einem Molekiildiagramm (die Wiener'sche Zahl) wird fur eine topologische Charakteriserung von kondensierten polyzyklischen Molekulsystemen angewandt. Dieser topologische Index unterscheidet wohl die isomerischen zyklischen Molekule. AusserClem widerspiegelt er auch in richtiger Weise ihre Struktureigenschaften. Mit Ausgangspunkt von diesen Begriffen werden die Hauptpunkte der molekularen Zyklicitat in 15 Regeln formulierl.
A procedure was developed, on the basis of the distance matrix of the graph, for the calculation of the specific π-electron energy and energy gap in polymerhomologous series and infinite polymers. 25 conjugated polymers were examined by this procedure and a fairly good correlation between these energy characteristics and the sum of all distances in the graph (the Wiener index) was found. A zero energy gap was shown to occur in 12 polymers. For polymers composed of condensed benzenoid and non-benzenoid cycles, a linear correlation was found between the Wiener index normalized to infinite polymer chains and the specific π-electron energy thus revealing possibilities for predictions proceeding from monomer topology only.
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