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.
Original language | English |
---|---|
Pages (from-to) | 90-111 |
Number of pages | 22 |
Journal | Journal of Combinatorial Theory. Series B |
Volume | 110 |
DOIs | |
Publication status | Published - 2015 Jan 1 |
Keywords
- Hoffman conjecture
- Hoffman graphs
- Line graphs
- Signed graphs
- Smallest eigenvalue
ASJC Scopus subject areas
- Theoretical Computer Science
- Discrete Mathematics and Combinatorics
- Computational Theory and Mathematics