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 TInew = ∑kN×PN(aN,bN,...) + kij×uij(aij,bij,cij). They were correlated to the boiling points of octanes. Using the mutually optimized combination of vertex-degree weighted path indices P2(a2,b2,c2), P3(a3,b3,c3,d3), and P4(a4,b4,c4,d4,e4) there was observed R = 0.99950. When in addition to P2(a2,b2,c2), P3(a3,b3,c3,d3), and P4(a4,b4,c4,d4,e4) also P1(a1,b1) or u72(a72,b72,c72) or u76(a76,b76,c76) or u62(a62,b62,c62) or u74(a74,b74,c74) or u52(a52,b52,c52) 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.

Keywords

• Boiling point
• Octanes
• Matrix elements
• Path indices
• Structural interpretation