Relations between topological indices of large chemical trees

Abstract

Several approximate relations have recently been established between molecular-graph-based structure descriptors of alkanes, in particular between (a) eigenvalue sum and Hosoya index. (b) greatest graph eigenvalue and connectivity index, (c) Wiener index and smallest positive Laplacian eigenvalue, (d) greatest Laplacian and greatest ordinary graph eigenvalue, (e) Zenkevich and Wiener index, and (f) hyper-Wiener and Wiener index. These all have been found to hold for alkanes with <i>n=</i>10<i> </i>or fewer carbon atoms, and have verified on samples consisting of all alkane isomers. Applying an algorithm for generating trees uniformly by random we have now tested these regularities for very large chemical trees (<i>n</i> =50). It has been found that regularities (c) and (f) hold equally well in the case of very large chemical trees, whereas regularities (a), (d) and (e) are applicable, but with significantly attenuated accuracy. Regularity (b) vanishes at large values of <i>n.</i>