Overall connectivity--a next generation molecular connectivity.

Area of Science:

• Cheminformatics
• Computational Chemistry
• Quantitative Structure-Property Relationships (QSPR)

Background:

• Molecular connectivity is a key concept in chemical graph theory.
• Existing methods like Randić's function and subgraph characterization have limitations.
• There is a need for advanced topological indices to capture molecular complexity.

Purpose of the Study:

• To analyze the development of molecular connectivity concepts.
• To introduce and define overall connectivity indices and related metrics.
• To demonstrate the utility of these novel indices in modeling physicochemical properties.

Main Methods:

• Analysis of Randić's inverse-square-root function and subgraph characterization.
• Development of definitions for overall connectivity index, eth-order overall connectivities, and overall connectivity vector.
• Calculation of topological indices for chemical graphs, including valence overall connectivities for heteroatom-containing molecules.
• Modeling physicochemical properties of alkanes using the novel indices.

Main Results:

• Overall connectivities increase with molecule size, branching, and cyclicity.
• Valence overall connectivities were constructed for molecules with heteroatoms.
• The novel indices demonstrated usefulness in modeling physicochemical properties of alkanes.
• Favorable comparisons were made with existing molecular connectivity and other probe connectivity functions.

Conclusions:

• The novel overall connectivity indices offer a promising advancement over existing molecular connectivity paradigms.
• These indices show significant potential for applications in quantitative structure-property/activity relationships (QSPR/QSAR).
• Revisiting the molecular connectivity paradigm is warranted based on these findings.