Computing degree based topological indices of algebraic hypergraphs

TL;DR

This paper introduces a new algebraic hypergraph structure based on prime ideal sums in commutative rings and calculates various topological indices for it.

Contribution

The novel contribution is defining a prime ideal sum hypergraph and computing degree-based topological indices for specific algebraic structures.

Findings

A new hypergraph structure based on prime ideal sums in commutative rings is introduced.

Several degree-based topological indices are computed for the defined hypergraphs.

Indices are calculated for specific cases of Zn with different prime factorizations.

Abstract

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∈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 Ei 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 Ei and Ei 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 Zn where n=pα,pq,p2q,p2q2,pqr,p3q, p2qr,pqrs for the distinct primes p,q,r and s.

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