Abstract
Trees have a simpler structure than general graphs, and we can prove stronger results. For example, interlacing tells us that the multiplicity of an eigenvalue decreases by at most one when a vertex is removed. For trees Godsil’s lemma gives the same conclusion also when a path is removed.
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© 2012 Andries E. Brouwer and Willem H. Haemers
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Brouwer, A.E., Haemers, W.H. (2012). Trees. In: Spectra of Graphs. Universitext. Springer, New York, NY. https://doi.org/10.1007/978-1-4614-1939-6_5
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DOI: https://doi.org/10.1007/978-1-4614-1939-6_5
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