A hypergraph extends an ordinary graph by allowing each edge to join an arbitrary nonempty subset of the vertex set. If one iterates the powerset construction further, one obtains nested (higher-order) vertex objects and, in turn, finite SuperHyperGraphs whose vertices and edges may be set-valued across multiple levels. Topological indices are numerical graph invariants-typically degree- or distance-based-that compactly encode structural information and often correlate with physical, chemical, or network properties. Among them, the Sombor index is a widely studied representative.
In this paper, we first review the Sombor index in the setting of SuperHyperGraphs. We then introduce two related notions, namely the Sombor index in Chemical SuperHyperGraphs and the Multiplicative Sombor index in SuperHyperGraphs, and we briefly examine their fundamental properties.