CLOSED-FORM EXPRESSIONS FOR DEGREE-BASED TOPOLOGICAL INDICES OF K_m⊙S_n

Abstract

We study degree-based topological indices for the corona product , where  is a complete graph and  is a star graph. Using the degree partition induced by the vertex types (core vertices of , the center of each star, and its leaves), we derive closed-form expressions for the first, second, and third Zagreb indices ; the Hyper-Zagreb index ; the Sigma index ; the Sombor index ; the Forgotten index ; and the SK-type descriptors . Our approach relies on edge-class decompositions and exact counting of degree contributions across the corona's three interaction layers (within , between  and star centers/leaves, and within stars). The resulting formulas reveal how parameters  and  govern connectivity, branching intensity, and degree heterogeneity in . We discuss asymptotic behavior in  and , identify dominant terms for large instances, and note consistencies with known special cases. The results provide analytically tractable descriptors for QSPR/QSAR applications and may guide the selection of indices suited to molecular structures exhibiting hub-leaf patterns.