Mathematics > Combinatorics
[Submitted on 14 May 2014 (v1), last revised 7 May 2015 (this version, v2)]
Title:Graphs with many valencies and few eigenvalues
View PDFAbstract:Dom de Caen posed the question whether connected graphs with three distinct eigenvalues have at most three distinct valencies. We do not answer this question, but instead construct connected graphs with four and five distinct eigenvalues and arbitrarily many distinct valencies. The graphs with four distinct eigenvalues come from regular two-graphs. As a side result, we characterize the disconnected graphs and the graphs with three distinct eigenvalues in the switching class of a regular two-graph.
Submission history
From: Edwin van Dam [view email][v1] Wed, 14 May 2014 07:09:18 UTC (10 KB)
[v2] Thu, 7 May 2015 12:42:12 UTC (20 KB)
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