**SOME
TOPOLOGICAL INDICES DERIVED FROM THE v**^{m}d^{n} 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^{m}d^{n}
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.