Abstract
A connected graph G is spectrally non-redundant if the spectral radiuses of the connected induced subgraphs of G are all different. As observed by Fernandes, Judice, and Trevisan (2017), for such graphs the number of connected induced subgraphs is equal to the number of complementarity eigenvalues. This note is an attempt at quantifying the so-called spectral redundancy phenomenon. Such a phenomenon occurs when there is a substantial amount of repetition among the spectral radiuses of the connected induced subgraphs.
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