Regularity and the Generalized Adjacency Spectra of Graphs
Regularity and the Generalized Adjacency Spectra of Graphs
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 …