MOLECULAR CYCLICITY AND CENTRICITY OF POLYCYCLIC GRAPHS .1. CYCLICITY BASED ON RESISTANCE DISTANCES OR RECIPROCAL DISTANCES

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 fibbons. The topological cyclicity patterns are thus reformulated in an extended basis, proceeding from three different graph metrics. (C) 1994 John Wiley & Sons, Inc.