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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.

In the present study, four detour matrix-based Topological Indices (TIs) termed as augmented path eccentric connectivity indices 1-4 (denoted by (AP)ξ(1)(C), (AP)ξ(2)(C), (AP)ξ(3)(C) and (AP)ξ(4)(C)) as well as their topochemical versions (denoted by (AP)ξ(1c)(C), (AP)ξ(2c)(C), (AP)ξ(3c)(C) and (AP)ξ(4c)(C)) have been conceptualised. A modified detour matrix termed as chemical detour matrix (Δ(c)) has also been proposed so as to facilitate computation of index values of topochemical versions of the said TIs. Values of the proposed TIs were computed for all the possible structures containing three, four and five vertices using an in-house computer program. The said TIs exhibited exceptionally high discriminating power and high sensitivity towards branching/relative position of substituent(s) in cyclic structures amalgamated with negligible degeneracy. Due care was taken during the development of TIs so as to ensure that reduction in index values of complex chemical structures to be within reasonable limits without compromising discriminating power. The mathematical properties of one of the proposed TIs have also been studied. With exceptionally high discriminating power, high sensitivity towards branching as well as relative position(s) of substituents in cyclic structures and negligible degeneracy, the proposed indices offer 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.