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Molecular cyclicity and centricity of polycyclic graphs. I. Cyclicity based on resistance distances or reciprocal distances
Author(s) -
Bonchev Danail,
Balaban Alexandru T.,
Liu Xiaoyu,
Klein Douglas J.
Publication year - 1994
Publication title -
international journal of quantum chemistry
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.484
H-Index - 105
eISSN - 1097-461X
pISSN - 0020-7608
DOI - 10.1002/qua.560500102
Subject(s) - reciprocal , wiener index , degeneracy (biology) , degenerate energy levels , molecular graph , mathematics , topological index , graph , combinatorics , physics , quantum mechanics , bioinformatics , philosophy , linguistics , biology
Abstract Rules for molecular cyclicity based on the global indices resulting from reciprocal distances (Harary number, H ) or from resistance distances (Kirchhoff number, Kf ) were tested in comparison with those elaborated earlier by means of the Wiener index, W . The Harary number and the Wiener number were found to match molecular cyclicity in an almost identical manner. The Kirchhoff number also generally follows cyclicity trends described previously. H is slightly less degenerate than is W , but Kf has practically no degeneracy in the graphs investigated here. Being much more discriminating than the Wiener number (i.e., practically nondegenerate), Kf allowed the formulation of new rules for systems formed from linearly condensed ribbons of even‐membered rings with different sizes as well as for branched ribbons. The topological cyclicity patterns are thus reformulated in an extended basis, proceeding from three different graph metrics. © 1994 John Wiley & Sons, Inc.