Mv. Diudea, WALK NUMBERS W-E(M) - WIENER-TYPE NUMBERS OF HIGHER RANK, Journal of chemical information and computer sciences, 36(3), 1996, pp. 535-540
Citations number
28
Categorie Soggetti
Information Science & Library Science","Computer Application, Chemistry & Engineering","Computer Science Interdisciplinary Applications",Chemistry,"Computer Science Information Systems
Definitions of Wiener W,(1) and hyper-Wiener R(2) numbers are reanalyz
ed and defined from a matrix-theoretical point of view. Thus, D and W-
1 (distance and Wiener,(3,4) of paths of length 1) matrices are recogn
ized as a basis for calculating W, whereas D-p and W-p (distance-path
[this work] and Wiener-path,(4) of paths of any length) are recognized
as a basis for the calculation of R. Weighted walk degrees W-e(M,i) g
enerated by an iterative additive algorithm(5) are considered as local
vertex invariants (LOVIs) whose half-sum in graph offers walk numbers
W-e(M), which are Wiener-type numbers of rank e; for e = 1, the class
ical W acid R numbers are obtained. New matrix invariants, Delta, D-p
(''combinatorial'' matrices constructed on D), K (of reciprocal [D-P](
ij) entries), and W-U (of unsymmetrical weighted distance) are propose
d as a basis for weighting walk degrees and whence for devising novel
numbers of Wiener-type.