THE Y-INDEX FOR DOUBLE CORONA OF GRAPHS RELATED TO THE DIFFERENT SUBDIVISION GRAPHS

Abstract

Abstract: Graph operations play a significant role in generating complex molecular and network structures from the simpler graphs. The computation of degree-based topological indices of such derived structure is an essential problem in chemical graph theory due to their applications in QSAR/QAPR studies. Among them, the Y index is a recently studied degree-based invariant that extends the family of Zagreb-type indices and captures structural information of graphs more efficiently. In this paper, we generalize the concepts of double corona graphs associated with subdivision-related graph operations and derive exact analytical expressions for the Y-index of these constructions. Closed-form formulae are obtained for the subdivision  and total graph based double corona products in terms of standard graph invariants and degree parameters. The obtained result extends the theoretical framework of degree-based indices under complex graph operations such as PANAM dendritic polymers and provide useful mathematical tools for modeling intricate molecular networks.