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(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.