SOME TOPOLOGICAL INDICES DERIVED FROM THE vmdn MATRIX.
PART 3. THE LARGEST EIGENVALUES OF THE vmdn MATRIX AS TOPOLOGICAL INDICES OF THE BIM-TYPE

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

Abstract
The L(m,n) indices are the largest eigenvalues of the vmdn matrix. Their properties are in many cases similar to properties of W(m,n) indices. The values of most, but not all tested L(m,n) indices increase with the size of the molecule. The increase is in general non-linear. Other structural features, e.g. the distance between the branches, the number of branches, and the type of branched structure have a substantial influence on the value of L(m,n) indices when the size of the molecule increases. The indices L(?,-) and L(-1,-) present no information about the properties of alkanes. The index L(0,0) presents only the information about the size of molecules. The index L(?,0) is a simple, primitive and degenerated, but a true branching index linking the BIM indices obeying the Methane based definition of branching with the BIA indices obeying the n-Alkane-based definition of branching. Several L(m,0) indices suggest 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 contrary is presented by the index L(2,0) and few other L(m,n) indices. The majority of other tested L(m,n) indices indicates that the isomers having branches closer to the centre of molecule are more branched, whereas those having a larger distance between branches are less branched. The L(m,n) indices are worse branching indices than the W(m,n) indices.