The full chracterazation of the graphs with a L-eigenvalue of multiplicity n-3

2017/12/01 by Daijun Yin, Qiongxiang Huang, Yin, Daijun +1
Chemistry · Mathematics · #05C50 #Combinatorics (math.CO) #FOS: Mathematics #Finite Group Theory Research #Graph theory and applications #Synthesis and Properties of Aromatic Compounds

paper · pdf · doi:10.48550/arxiv.1712.00208

openalex publication_date 2017/12/01 · openalex created_date 2017/12/22 · openalex updated_date 2026/07/28

Abstract

Let G(n,k) be the set of connected graphs of order n with one of the Laplacian eigenvalue having multiplicity k. It is well known that G(n,n-1)=\K_n\. The graphs of G(n,n-2) are determined by Das, and the graphs of G(n,n-3) with four distinct Laplacian eigenvalues are determined by Mohammadian et al. In this paper, we determine the graphs of G(n,n-3) with three distinct Laplacian eigenvalues, and then the full characterization of the graphs in G(n,n-3) is completed.

Citations

• Complement reducible graphs

Related

• Full characterization of graphs having certain normalized Laplacian eigenvalue of multiplicity n-3
• On graphs with m(∂^L₁)=n-3
• Characterization of graphs with some normalized Laplacian eigenvalue of multiplicity n-3
• On graphs with some normalized Laplacian eigenvalue of extremal multiplicity
• Girth and Laplacian eigenvalue distribution