On Intersection Graph of Dihedral Group

2020/11/20 by Sanhan Muhammad Salih Khasraw, Khasraw, Sanhan
Computer Science · Mathematics · #Advanced Graph Theory Research #Combinatorics (math.CO) #FOS: Mathematics #Graph Labeling and Dimension Problems #Graph theory and applications

paper · pdf · doi:10.48550/arxiv.2011.10544

openalex publication_date 2020/11/20 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Let G be a finite group. The intersection graph of G is a graph whose vertex set is the set of all proper non-trivial subgroups of G and two distinct vertices H and K are adjacent if and only if H∩ K ≠ \e\, where e is the identity of the group G. In this paper, we investigate some properties and exploring some topological indices such as Wiener, Hyper-Wiener, first and second Zagreb, Schultz, Gutman and eccentric connectivity indices of the intersection graph of D_2n for n=p², p is prime. We also find the metric dimension and the resolving polynomial of the intersection graph of D_2p².

Related

• Intersection Hypergraph on D_n
• Connectivity of Intersection Graphs of Finite Groups
• On the diameter of intersection graphs of finite groups
• Toroidality and projective-planarity of intersection graphs of subgroups of finite groups
• Intersection graph of cyclic subgroups of groups