The graphs with exactly two distance eigenvalues different from −1 and −3
Abstract
In this paper, we completely characterize the graphs with third largest distance eigenvalue at most $-1$ and smallest distance eigenvalue at least $-3$. In particular, we determine all graphs whose distance matrices have exactly two eigenvalues (counting multiplicity) different from $-1$ and $-3$. It turns out that such graphs consist of three infinite classes, and all of them are determined by their distance spectra. We also show that the friendship graph is determined by its distance spectrum.
Type
Publication
In Journal of Algebraic Combinatorics
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Lu Lu(鲁卢)
Associate Professor, PhD Supervisor
My research interests include algebraic graph theory, spectral graph theory and group theory.