Edge-signed graphs with smallest eigenvalue greater than -2
Combinatorics
2015-01-08 v2
Abstract
We give a structural classification of edge-signed graphs with smallest eigenvalue greater than -2. We prove a conjecture of Hoffman about the smallest eigenvalue of the line graph of a tree that was stated in the 1970s. Furthermore, we prove a more general result extending Hoffman's original statement to all edge-signed graphs with smallest eigenvalue greater than -2. Our results give a classification of the special graphs of fat Hoffman graphs with smallest eigenvalue greater than -3.
Keywords
Cite
@article{arxiv.1309.5178,
title = {Edge-signed graphs with smallest eigenvalue greater than -2},
author = {Gary Greaves and Jack Koolen and Akihiro Munemasa and Yoshio Sano and Tetsuji Taniguchi},
journal= {arXiv preprint arXiv:1309.5178},
year = {2015}
}
Comments
25 pages