SOME TOPOLOGICAL INDICES DERIVED FROM THE vmdn MATRIX. PART 1. WIENER-LIKE INDICES OF THE BIM-TYPE

Anton Perdih,* Branislav Perdih
Mala vas 12, SI-1000 Ljubljana, Slovenia

ABSTRACT

The matrix having nondiagonal elements vmdn (vmdn matrix) is a step in unification of several matrices used to derive topological indices, i.e. of the adjacency matrix, the distance matrix, the reciprocal distance matrix, etc. From the vmdn matrix were derived 225 Wiener-like indices W(m,n). All of them are of the BIM-type, i.e. they obey the Methane-based definition of branching. The index W(?,-) links the BIM indices with the BIA indices obeying the n-Alkane-based definition of branching. It is a simple, primitive, and degenerated, but a true branching index showing that the presence and the number of methyl groups (vertices of degree one) is of the highest importance in branching (complexity) of molecules. The index W(-,0) contains also the information of the size of a molecule. The indices W(1,0), W(0,0), W(0,-), and W(-1,-) only present information about the size of molecules. Most of the W(m,?) and W(m,0) indices contain also the information that a branch on a quaternary carbon (i.e. on a vertex of degree four) contributes more to branching (complexity) than a branch on a tertiary carbon (i.e. on a vertex of degree three). The indices W(?,n) and W(0,n) present, besides information about the size of a molecule and the number of branches, also information about the position of branches and the distance between them. Other W(m,n) indices present different, in some cases quite extreme combinations of all these parts of information.