TOPOLOGICAL DESCRIPTORS OF LINE GRAPHS IN POLYMER SUPRAMOLECULAR NETWORKS

Abstract

This research provides the graph theoretical study for a polymer supramolecular network within the paradigm of deriving various degree-based topological invariants through the constructed line graph representation for the underlying supramolecular structure. Networks comprised of supramolecular structures, which are based on non-covalent bonds, are difficult to represent within the conventional graph representation paradigm because they are dynamic in nature and have non-covalent bonds within the network. The line graph transformation paradigm has been adopted with the supramolecular structure for a more appropriate representation of such complex systems’ structure and connectivity within the underlying graph representation paradigm. These indices form the cornerstone of robust quantitative structure property relationship and quantitative structure activity relationship. The derivation of various important topological invariants, such as the Randić index, Zagreb index, and Harmonic index, provides the bridge for a quantitative relationship between the supramolecular network structures and various functional groups and behaviors within a deterministic paradigm for such complex networks and structures.

Keywords : Topological indices; Line graph; Polymer Supramolecular Network.