Hypergraph-Theoretic Perspectives on Prime Ideal Sum Graphs

Abstract

Graph models are effective for capturing pairwise relationships in relational data, but many real-world relationships involve multiple entities and may be more accurately represented using hypergraphs. Consequently, the construction and analysis of hypergraph models for algebraic structures has recently attracted growing interest among algebraists. Motivated by this fact, in this work we study the hypergraph version of prime ideal sum graphs. As part of our investigation, we delved into the hypergraph-theoretic properties of completeness, connectedness, diameter, and girth concepts. Furthermore, we analyzed the homomorphic and isomorphic characteristics of these hypergraphs. At the end, we give an algorithmic design to obtain the decomposition sets of the hyperedges of a prime ideal sum hypergraph over Z_n which can be developed to compute the topological parameters of the graph directly.