Intersection hypergraph on Dn

Let [Formula: see text] be a group and [Formula: see text] be the set of all nontrivial proper subgroups of [Formula: see text]. The intersection hypergraph of [Formula: see text] , denoted by [Formula: see text], is a hypergraph whose vertex set is [Formula: see text] 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, [Formula: see text]. We examine some of the structural properties, viz., diameter, girth and chromatic number of [Formula: see text]. Also, we provide characterizations for hypertrees, star structures of [Formula: see text], and investigate the planarity and nonplanarity of [Formula: see text].