• Corpus ID: 239024379

# On the minimum number of distinct eigenvalues of a threshold graph

@inproceedings{Fallat2021OnTM,
title={On the minimum number of distinct eigenvalues of a threshold graph},
author={Shaun M. Fallat and Seyed Ahmad Mojallal},
year={2021}
}
• Published 19 October 2021
• Mathematics
For a graph G, we associate a family of real symmetric matrices, S (G), where for any A ∈ S (G), the location of the nonzero off-diagonal entries of A are governed by the adjacency structure of G. Let q(G) be the minimum number of distinct eigenvalues over all matrices in S (G). In this work, we give a characterization of all connected threshold graphs G with q(G) = 2. Moreover, we study the values of q(G) for connected threshold graphs with trace 2, 3, n − 2, n − 3, where n is the order of…

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