engleski

On the Novel Balaban-like and Balaban-Detour-like Molecular Descriptors

Novel Balaban-like and Balaban-detour-like topological indices are introduced. Starting from the original form of the Balaban index J in [1] where the summand is defined as (didj)-1/2, we defined three modifications named Balaban-like indices with the summands (didj)1/2, (di + dj)-1/2, and [didj/(di + dj)]1/2, and symbolized as Jm1, Jm2, and Jm3, respectively. In these mathematical formulae i and j are adjacent vertices, and di and dj are distance-sums (or distance-degree) of the shortest distances of vertices i and j to all other vertices in the graph representing molecular skeleton. In these topological indices summations are performed over all connected pairs of vertices. Analogously, the Balaban-detour index D = (δiδj)-1/2 based on distance-sums of the longest distances of vertices to all other vertices in molecular graph (δi and δj) is defined, together with three modifications of D named Balaban-detour-like indices with the summands (δiδj)1/2, (δi + δj)-1/2, and [δiδj/(δi + δj)]1/2 and symbolized as Dm1, Dm2, and Dm3. For a given pair of connected vertices i and j, the value of a summand is the contribution (weight) of the corresponding bond between vertices i and j to the total index value. Thus, different functional forms of summand give different numerical contributions of the same bond in calculating the values of topological indices introduced in this study. Relationship between introduced novel variants of Balaban indices and the original Balaban index, as well as their relationships with several physico-chemical properties are analyzed on several data sets, including the one that was used for introduction of the original Balaban index in [1]. These correlational analyses are performed both on linear and on logarithmic scale, in order to explore the existence of both linear and nonlinear relationships. The correlations and analyses performed indicate that the novel topological indices introduce an additional, mostly nonlinear, information. From comparative correlational analyses performed on several data sets, it is concluded that these novel topological indices have reasonable potential for their valuable use as molecular descriptors in structure-property modeling.

Balaban-like topological indices ; Balaban-detour-like topological indices ; acyclic hydrocarbons ; cyclic hydrocarbons ; benzenoid hydrocarbons ; nonlinear relationship ; one-descriptor model ; comparative correlation study

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