Co-maximal Hypergraph on Dn

2025/04/30 by Sachin Ballal, Ballal, Sachin, A N Ardra +1
Engineering · Mathematics · #05C25 #05C65 #Combinatorics (math.CO) #FOS: Mathematics #Finite Group Theory Research #Limits and Structures in Graph Theory #graph theory and CDMA systems

paper · pdf · doi:10.48550/arxiv.2504.21554

openalex publication_date 2025/04/30 · 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 co-maximal hypergraph of G, denoted by Co_H(G), is a hypergraph whose vertex set is \H ∈ S | H K = G for some K ∈ S \ and hyperedges are the maximal subsets of the vertex set with the property that the product of any two vertices is equal to G. The aim of this paper is to study the co-maximal hypergraph of dihedral groups, Co_H(D_n). We examine some of the structural properties, viz., diameter, girth and chromatic number of Co_H(D_n). Also, we provide characterizations for hypertrees, star structures and 3-uniform hypergraphs of Co_H(D_n). Further, we discuss the possibilities of Co_H(D_n) which can be embedded on the plane, torus and projective plane.

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