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

Rules for molecular cyclicity based on the global indices resulting fr om reciprocal distances (Harary number, H) or from resistance distance s (Kirchhoff number, Kf) were tested in comparison with those elaborat ed earlier by means of the Wiener index, W. The Harary number and the Wiener number were found to match molecular cyclicity in an almost ide ntical manner. The Kirchhoff number also generally follows cyclicity t rends described previously. H is slightly less degenerate than is W, b ut Kf has practically no degeneracy in the graphs investigated here. B eing much more discriminating than the Wiener number (i.e., practicall y nondegenerate), Kf allowed the formulation of new rules for systems formed from linearly condensed ribbons of even-membered rings with dif ferent sizes as well as for branched fibbons. The topological cyclicit y patterns are thus reformulated in an extended basis, proceeding from three different graph metrics. (C) 1994 John Wiley & Sons, Inc.