On Intersection and Co-maximal Hypergraph of ℤ_n

2025/09/18 by Sachin Ballal, Ballal, Sachin, A N Ardra +1
Mathematics · #05C25 #05C65 #Advanced Topology and Set Theory #Combinatorics (math.CO) #FOS: Mathematics #Finite Group Theory Research #Group Theory (math.GR) #Limits and Structures in Graph Theory

paper · pdf · doi:10.48550/arxiv.2509.14618

openalex publication_date 2025/09/18 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

The aim of this paper is to study the intersection hypergraph Γ_H(ℤ_n) and co-maximal hypergraph Co_H(ℤ_n) on the subgroups of ℤ_n. We prove that the intersection and co-maximal hypergraph of a finite abelian group are isomorphic. Hence, we focus on Γ_H(ℤ_n) and examine some of the structural properties, viz., diameter, girth and chromatic number of Γ_H(ℤ_n). Also, we provide characterizations for hypertrees, star structures of Γ_H(ℤ_n), and investigate the planarity and non-planarity of Γ_H(ℤ_n).

Citations

• Hypergraphs defined on algebraic structures
• Graphs defined on groups

Related

• Intersection Hypergraph on D_n
• Co-maximal Hypergraph on Dn
• The quasi-isometry invariance of the Coset Intersection Complex
• Toroidality and projective-planarity of intersection graphs of subgroups of finite groups
• Maximal intersections in finite groups