SOME TOPOLOGICAL INDICES DERIVED FROM THE v^mdⁿ MATRIX. PART 9. THE Mj(m,n) AND Mij(m,n) INDICES

Anton Perdih,* Branislav Perdih

Mala vas 12, SI-1000 Ljubljana, Slovenia

Abstract

The Mj(m,n) and Mij(m,n) indices considered here are derived from the v^mdⁿ matrix by multiplication of its non-diagonal elements. A general characteristic of the Mj(m,n) and Mij(m,n) indices is the transition domain in the plane of exponents m and n, which is placed along the diagonal characterized by m = -n. Above this diagonal transition domain the values of the Mj(m,n) and Mij(m,n) indices of alkanes increase with the size of the molecule and decrease with branching, whereas the reverse is true below the diagonal. Correlation of tested Mj(m,n) and Mij(m,n) indices with the physicochemical properties of alkanes is better than ïrï = 0.9 in 15 resp. 13 of 23 cases when alkanes from propane to octanes inclusive are considered, as well as in 12 resp. 8 of 24 cases when only octanes are taken into account. There is a number of Mj(m,n) and Mij(m,n) indices that have a regular sequence of isomers due to increasing branching. In the plane of exponents m and n they are positioned in the regions characterized by m £ -1, -1 £ n < 1 and m ³ 1, -1 < n £ 1 among the Mj(m,n) indices, as well as -6 £ m £ ¹/₃, -4 £ n < 1 and m ³ ¹/₃, -1 < n £ 2 among the Mij(m,n) indices.