Abstract
Vertex degree weighted path indices P(N)(a, b, ...), for example P(1)(a, b), P(2)(a, b, c), P(3)(a, b, c, d), and P(4)(a, b, c, d, e), are good topological indices for some of the physicochemical properties of octanes with |R|(max) up to 0.999. Mutually optimized combinations of them are even better, R (P(1)..P(4)) is in the worst tested case > 0.9. The best results are obtained in mutually optimized combinations of some of them with some of the elements of the Universal matrix, in the worst tested case R = 0.994. Some of the vertex degree weighted path one indices give rise to a "regular" sequence of octane isomers of increasing branching.
Highlights
IntroductionPath indices are an eminent group of topological indices and together with the connectivity indices they are frequently used, starting by Wiener and followed by several other authors
Path indices1,2 are an eminent group of topological indices and together with the connectivity indices3–6 they are frequently used, starting by Wiener7,8 and followed by several other authors.In a private discussion about topological indices, Prof
The best results are obtained in mutually optimized combinations of some of them with some of the elements of the Universal matrix, in the worst tested case R = 0.994
Summary
Path indices are an eminent group of topological indices and together with the connectivity indices they are frequently used, starting by Wiener and followed by several other authors. In a private discussion about topological indices, Prof. M. Randi} suggested to study the path indices in a similar way as there were studied the indices derived from the Universal matrix U(a, b, c), and there should be tested the combinations of them. Randi} suggested to study the path indices in a similar way as there were studied the indices derived from the Universal matrix U(a, b, c), and there should be tested the combinations of them The results of this approach are presented below.
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