On graphs with $m(\partial^L_1)=n-3$

Lu Lu; Qiongxiang Huang; Xueyi Huang

On graphs with $m(\partial^L_1)=n-3$

Combinatorics 2017-04-12 v1

Authors: Lu Lu , Qiongxiang Huang , Xueyi Huang

Abstract

Let $\partial^L_1\ge\partial^L_2\ge\cdots\ge\partial^L_n$ be the distance Laplacian eigenvalues of a connected graph $G$ and $m(\partial^L_i)$ the multiplicity of $\partial^L_i$ . It is well known that the graphs with $m(\partial^L_1)=n-1$ are complete graphs. Recently, the graphs with $m(\partial^L_1)=n-2$ have been characterized by Celso et al. In this paper, we completely determine the graphs with $m(\partial^L_1)=n-3$ .

Keywords

graph laplacian spectral graph theory graph theory

Cite

@article{arxiv.1704.03122,
  title  = {On graphs with $m(\partial^L_1)=n-3$},
  author = {Lu Lu and Qiongxiang Huang and Xueyi Huang},
  journal= {arXiv preprint arXiv:1704.03122},
  year   = {2017}
}

Comments

13 pages, 3 figures

Related papers

View all related →