Usefulness of Combinations of Vertex-Degree Weighted Path Indices and Elements of a Universal Matrix

Abstract

The mutually optimized combinations of vertex-degree weighted path indices and the vertex-degree vertex-distance weighted elements of the Universal matrix were applied in the way of TI new = ∑k N ×PN(a N ,b N ,...) + k ij ×u ij (a ij ,b ij ,c ij). They were correlated to the boiling points of octanes. Using the mutually optimized combination of vertex-degree weighted path indices P2(a 2 ,b 2 ,c 2), P3(a 3 ,b 3 ,c 3 ,d 3), and P4(a 4 ,b 4 ,c 4 ,d 4 ,e 4) there was observed R = 0.99950. When in addition to P2(a 2 ,b 2 ,c 2), P3(a 3 ,b 3 ,c 3 ,d 3), and P4(a 4 ,b 4 ,c 4 ,d 4 ,e 4) also P1(a 1 ,b 1) or u 72 (a 72 ,b 72 ,c 72) or u 76 (a 76 ,b 76 ,c 76) or u 62 (a 62 ,b 62 ,c 62) or u 74 (a 74 ,b 74 ,c 74) or u 52 (a 52 ,b 52 ,c 52) have been applied, then the goodnesses of up to R = 0.99988, S = 0.098, IC = 98.5% have been observed. The mutually optimized combinations of vertex-degree weighted path indices and the vertex-degree vertex-distance weighted elements of the Universal matrix are promising indices also for other physicochemical properties of octanes.

Physicochemical Properties of Octane Isomers in View of the Structural Numbers

“…19 To obtain better correlations, the mutually optimized combinations of vertex-degree vertex-distance weighted elements of the Universal matrix and vertex-degree weighted path indices are to be used. 15,[20][21][22] As shown above, the values of the mutually optimized factors k Ni as well as of products IC×|k Ni | are useful for the structural interpretation of the values of physicochemical properties of octanes, as well. Whereas in the best case, i.e.…”