Randic connectivity index

The Randic connectivity index, X, is also called the connectivity index or branching index, and is defined by Eq. (18) [7], where b runs over the bonds i-j of the molecule, and and dj are the vertex degrees of the atoms incident with the considered bond. 

Several physical properties of benzenoid hydrocarbons can be correlated with a function of the molecular connectivity of their equivalent Gutman trees. Namely, we use the Randic connectivity index [32], x, viz.,... 

Figure 9 shows a correlation between the heats of atomizations [37] of two families of unbranched hydrocarbons and the Randic connectivity index of their equinumerical (equivalent) caterpillars. 

J2) cj, where the sum runs over the occupied MOs for a single AO. The molecular mass is represented by M, and is the Randic connectivity index of order 3. 

Other encountered graphical bond order descriptors are the /V/ index, the W AV index, the WW AVW index, the J7J index, the CID7CID index, and the - Z7Z index derived, respectively, from the - Randic connectivity index, the -> Wiener index, the - hyper-Wiener index, the - Balaban distance connectivity index, the - Randic connectivity ID number, and the Hosoya Z index. 

Bowden-Young steric constant steric descriptors (O Charton steric constant) branching index Randic connectivity index - connectivity indices branching layer matrix layer matrices... 

Another topological descriptor specifically proposed for cis/trans isomerism is the Pogliani cis/trans connectivity index xcr> defined in terms of the - Randic connectivity index y as ... 

This interpretation places emphasis on the bimolecular encounter possibility among molecules, reflecting the collective influence of the bond accessibilities of each molecule with other molecules in its immediate environment. Therefore, the Randic connectivity index can be interpreted as the contribution of one molecule to the bimolecular interaction arising from the encounters of bonds of two identical molecules ... 

The mean Randic connectivity index (or mean Randic branching index) is defined as ... 

A variant of the Randic connectivity index was also proposed as ... 

Molecular descriptor proposed as the sum of atomic properties, accounting for valence electrons and extended connectivities in the H-depleted molecular graph using a Randic connectivity index-type formula [Lohninger, 1993] ... 

These are modifications of the Randic connectivity index defined in such a way as to account for the presence of heteroatoms in the molecule [Kupchik, 1986 Kupchik, 1988 Kupchik, 1989] ... 

From the edge adjacency matrix, a graph-theoretical invariant analogous to the -> Randic connectivity index was derived by Estrada [Estrada, 1995a] it is called edge connectivity index, denoted by e, and defined as ... 

Molecular descriptors defined in analogy with the - Randic connectivity index and calculated on hydrogen-included molecular graphs where heavy vertices are weighted by valence group electronegativities [Diudea et al, 1996a]. 

Wiener index Zagreb indices Randic connectivity index Hosoya Z index... 

A vector of molecular topological descriptors can be calculated for the whole iterated line graph sequence. For example, a line graph Randic connectivity index was calculated as ... 

The first term % coincides with the - Randic connectivity index x the remaining values show monotonically smaller values. In acyclic graphs, the even powers of matrices necessarily make zero contributions as it is not possible to reach an adjacent vertex by an even number of steps. 

The map connectivity matrices are another set of map matrices based on partitioning of the —> Randic connectivity index and the higher order —> connectivity indices into contributions arising from paths of length k [Randic and Basak, 2002]. They are defined as... 

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