For every rational number x 2 (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.
|Place of Publication||Tilburg|
|Number of pages||6|
|Publication status||Published - 2005|
|Name||CentER Discussion Paper|