Abstract
Let B(n, k) be the subgraph of the Boolean lattice BLn induced by the kth and (k + 1)th layers. The distance spectrum of BLn was obtained by Aalipour et al. and Koolen et al. proved that BLn is determined by its distance spectrum. In this paper, we introduce a new method to verify that a quotient matrix contains all distance eigenvalues of a graph, and we get the distance spectrum of B(n, k) by using this method. It is proved that B(n, k) has exactly four distinct distance eigenvalues, and its diameter can be arbitrarily large.
Type
Publication
In Linear and Multilinear Algebra
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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.