The generating graph of dicyclic groups
Abstract
For a group G, the generating graph of G, denoted by Γ(G). We define Qn=⟨x,y:x2n=y4=1,xn=y2,y−1xy=x−1⟩, the dicyclic group of order 4n. This paper primarily explores the graph characteristics and spectral properties of various matrices associated with Γ(Qn). Specifically, we determine the complete spectrum of the adjacency, Laplacian, distance and eccentricity matrices. Additionally, we completely determine the spectrum of the distance and eccentricity matrices of the dihedral group of order 2n, denoted as Dn.
Fields of Study & Subjects
Graph theory and applications
Publication details
- Journal / source
- Linear and Multilinear Algebra
- Publisher
- Informa UK Limited
- Volume
- 74
- Issue
- 4
- Pages
- 383–407
- Publication date
- 11 February 2026
- Language
- EN