Computing degree based topological indices of algebraic hypergraphs

Topological indices are numerical parameters that indicate the topology of graphs or hypergraphs. A hypergraph H = (V (H), E(H)) consists of a vertex set V (H) and an edge set E(H), where each edge e is an element of E(H) is a subset of V(H) with at least two elements. In this paper, our main aim is to introduce a general hypergraph structure for the prime ideal sum (PIS)- graph of a commutative ring. The prime ideal sum hypergraph of a ring R is a hypergraph whose vertices are all non-trivial ideals of R and a subset of vertices E, with at least two elements is a hyperedge whenever I + J is a prime ideal of R for each non-trivial ideal I, J in E, and E, is maximal with respect to this property. Moreover, we also compute some degree-based topological indices (first and second Zagreb indices, forgotten topological index, harmonic index, Randic index, Sombor index) for these hypergraphs. In particular, we describe some degree-based topological indices for the newly defined algebraic hypergraph based on prime ideal sum for Z(n) where n = p(alpha), pq, p(2)q, p(2)q(2), pqr, p(3)q, p(2)qr, pqrs for the distinct primes p, q, r and s.