| Article ID | Journal | Published Year | Pages | File Type |
|---|---|---|---|---|
| 4602999 | Linear Algebra and its Applications | 2006 | 5 Pages |
Abstract
For every rational number x ∈ (0, 1), we construct a pair of graphs, one regular and one nonregular with adjacency matrices A1 and A2, having the property that A1 − xJ and A2 − xJ have the same spectrum (J is the all-ones matrix). This solves a problem of Van Dam and the second author. For some values of x, we have generated the smallest examples (with respect to the number of vertices) by computer.
Related Topics
Physical Sciences and Engineering
Mathematics
Algebra and Number Theory
