Detour matrix-based adjacent path eccentric distance sum indices for QSAR/QSPR. Part I: development and evaluation.

In the present study, three detour matrix-based topological indices (TIs) termed as adjacent path eccentric distance sum indices 1-3 (denoted by (A)ξ(1)(PDS), (A)ξ(2)(PDS) and (A)ξ(3)(PDS)) as well as their topochemical versions (denoted by (A)ξ(1c)(PDS), (A)ξ(2c)(PDS) and (A)ξ(3c)(PDS)) have been conceptualised. Values of the proposed TIs were computed for all possible cyclic and acyclic structures containing three, four, five vertices using an in-house computer programme. Proposed TIs were evaluated for discriminating power, degeneracy, intercorrelation and sensitivity towards branching as well relative position of substituent(s) in cyclic structures. Mathematical properties of one of the proposed TIs were also studied. Exceptionally high discriminating power, high sensitivity towards branching as well as relative position(s) of substituent(s) in cyclic structures and negligible degeneracy offer proposed indices a vast potential for use in characterisation of structures, similarity/dissimilarity studies, lead identification and optimisation, combinatorial library design and quantitative structure-activity/property/toxicity/pharmacokinetic relationship studies so as to facilitate drug design.