On the spectrum of an equitable quotient matrix and its application

By Lihua You, Man Yang, Wasin So, Weige Xi. Linear Algebra and its Applications, 2019

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Abstract Let M be a partitioned matrix and B be its equitable quotient matrix. In this paper, we prove the inclusion of their spectra σ ( B ) ⊆ σ ( M ) , and the equality of their spectral radii ρ ( B ) = ρ ( M ) if M is nonnegative. Moreover, σ ( M ) is shown to be completely determined by σ ( B ) if M is from a class of special matrices. Then we apply these results to obtain the spectra of some well-known matrices associated with graphs or digraphs, and then determine the extremal values of different spectral radii associated with connected graphs or strongly connected digraphs with given vertex connectivity.

Subfields: Computational Theory and Mathematics, Geometry and Topology

View Paper: https://www.semanticscholar.org/paper/4dfbee171de85319deb34eb01c424a7ebe22192b