Intersection Hypergraph on D_n
Sachin Ballal, Ardra A N

TL;DR
This paper investigates the intersection hypergraph of dihedral groups, analyzing its structural properties such as diameter, girth, chromatic number, and planarity, and characterizes special structures like hypertrees and stars.
Contribution
It provides a detailed study of the intersection hypergraph of dihedral groups, including structural properties and characterizations of specific hypergraph configurations.
Findings
Determined the diameter, girth, and chromatic number of the hypergraph.
Characterized hypertrees and star structures within the hypergraph.
Analyzed the planarity and non-planarity conditions of the hypergraph.
Abstract
Let be a group and be the set of all non-trivial proper subgroups of . The intersection hypergraph of , denoted by , is a hypergraph whose vertex set is 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, . We examine some of the structural properties, viz., diameter, girth and chromatic number of . Also, we provide characterizations for hypertreees, star structures of , and investigate the planarity and non-planarity of .
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Taxonomy
TopicsComputational Geometry and Mesh Generation
