Computing degree based topological indices of algebraic hypergraphs.

Topological indices are numerical parameters that indicate the topology of graphs or hypergraphs. A hypergraph consists of a vertex set and an edge set , where each edge is a subset of 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 is a hypergraph whose vertices are all non-trivial ideals of and a subset of vertices with at least two elements is a hyperedge whenever is a prime ideal of for each non-trivial ideal , in and 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, Randić 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 where , for the distinct primes and .