Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
4656809 | Journal of Combinatorial Theory, Series B | 2015 | 22 Pages |
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.
Related Topics
Physical Sciences and Engineering
Mathematics
Discrete Mathematics and Combinatorics
Authors
Gary Greaves, Jack Koolen, Akihiro Munemasa, Yoshio Sano, Tetsuji Taniguchi,