Applications of analysis to the determination of the minimum number of distinct eigenvalues of a graph

2017/08/05 by Bjorkman, Beth, Hogben, Leslie, Ponce, Scarlitte +2
#05C50 #15A18 #15A29 #15B57 #26B10 #58C15 #Combinatorics (math.CO) #FOS: Mathematics

paper · doi:10.48550/arxiv.1708.01821

Abstract

We establish new bounds on the minimum number of distinct eigenvalues among real symmetric matrices with nonzero off-diagonal pattern described by the edges of a graph and apply these to determine the minimum number of distinct eigenvalues of several families of graphs and small graphs.

Related

• Minimum number of distinct eigenvalues of graphs
• The minimum number of distinct eigenvalues of a threshold graph is at most 4
• Bordering of Symmetric Matrices and an Application to the Minimum Number of Distinct Eigenvalues for the Join of Graphs
• Minimum number of distinct eigenvalues of distance-regular and signed Johnson graphs
• On the minimum number of distinct eigenvalues of triangle-free strongly regular graphs