Graphs of order $n$ and diameter $2(n-1)/3$ minimizing the spectral radius

Jingfen Lan; Lingsheng Shi

Graphs of order $n$ and diameter $2(n-1)/3$ minimizing the spectral radius

Spectral Theory 2014-05-21 v1 Combinatorics

Authors: Jingfen Lan , Lingsheng Shi

Abstract

The spectral radius of a graph is the largest eigenvalue of its adjacency matrix. A minimizer graph is such that minimizes the spectral radius among all connected graphs on $n$ vertices with diameter $d$ . The minimizer graphs are known for $d\in\{1,2\}\cup [n/2,2n/3-1]\cup\{n-k\mid k=1,2,...,8\}$ . In this paper, we determine all minimizer graphs for $d=2(n-1)/3$ .

Keywords

spectral radius adjacency matrix graph diameter minimizer graphs eigenvalues connected graphs extremal graph theory

Cite

@article{arxiv.1405.5015,
  title  = {Graphs of order $n$ and diameter $2(n-1)/3$ minimizing the spectral radius},
  author = {Jingfen Lan and Lingsheng Shi},
  journal= {arXiv preprint arXiv:1405.5015},
  year   = {2014}
}

Comments

13 pages

Related papers

View all related →