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A new class of distance–based molecular structure descriptors is put forward, aimed at eliminating a general shortcoming of the Wiener and Wiener–type indices, namely that the greatest contributions to their numerical values come from vertex pairs at greatest distance. The Q-indices, considered in this work, consist of contributions of vertex pairs that(More)
A secondary structure is a planar, labeled graph on the vertex set {1; : : : ; n} having two kind of edges: the segments [i; i + 1], for 1 6 i 6 n − 1 and arcs in the upper half-plane connecting some vertices i; j, i 6 j, where j − i ¿ l, for some ÿxed integer l. Any two arcs must be totally disjoint. We enumerate secondary structures with respect to their(More)
Valence-weightings are considered for shortest-path distance moments, as well as related weightings for the so-called " Wiener " polynomial. In the case of trees the valence-weighted quantities are found to be expressible as a combination of unweighted quantities. Further the weighted quantities for a so-called " thorny " graph are considered and shown to(More)
Two general methods for establishing the logarithmic behavior of recursively defined sequences of real numbers are presented. One is the interlacing method, and the other one is based on calculus. Both methods are used to prove logarithmic behavior of some combinatorially relevant sequences, such as Motzkin and Schröder numbers, sequences of values of some(More)