Intersection Hypergraph on D_n

2025/02/14 by Sachin Ballal, Ballal, Sachin, A N Ardra +1
Computer Science · #Combinatorics (math.CO) #Computational Geometry and Mesh Generation #FOS: Mathematics #Group Theory (math.GR)

paper · pdf · doi:10.48550/arxiv.2502.10117

openalex publication_date 2025/02/14 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Let G be a group and S be the set of all non-trivial proper subgroups of G. The intersection hypergraph of G, denoted by Γ_H(G), is a hypergraph whose vertex set is \H ∈ S | H ∩ K = \e\ for some K ∈ S \ and hyperedges are the maximal subsets of the vertex set with the property that any two vertices in it have a trivial intersection. The aim of this paper is to study the intersection hypergraph of dihedral groups, Γ_H(D_n). We examine some of the structural properties, viz., diameter, girth and chromatic number of Γ_H(D_n). Also, we provide characterizations for hypertreees, star structures of Γ_H(D_n), and investigate the planarity and non-planarity of Γ_H(D_n).

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