@techreport{abb5a199ef7c44019efff8387886a381,

title = "Regularity and the Generalized Adjacency Spectra of Graphs",

abstract = "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.",

keywords = "graphs, matrices",

author = "A.A. Chesnokov and W.H. Haemers",

note = "Pagination: 6",

year = "2005",

language = "English",

volume = "2005-124",

series = "CentER Discussion Paper",

publisher = "Operations research",

type = "WorkingPaper",

institution = "Operations research",

}