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Title: Interlacing families and the Hermitian spectral norm of digraphs
Authors: Greaves, Gary Royden Watson
Mohar, Bojan
O, Suil
Keywords: Science::Mathematics
Issue Date: 2018
Source: Greaves, G. R. W., Mohar, B., & O, S. (2019). Interlacing families and the Hermitian spectral norm of digraphs. Linear Algebra and its Applications, 564, 201-208. doi:10.1016/j.laa.2018.12.004
Journal: Linear Algebra and its Applications
Abstract: It is proved that for any finite connected graph $G$, there exists an orientation of $G$ such that the spectral radius of the corresponding Hermitian adjacency matrix is smaller or equal to the spectral radius of the universal cover of $G$ (with equality if and only if $G$ is a tree). This resolves a problem proposed by Mohar. The proof uses the method of interlacing families of polynomials that was developed by Marcus, Spielman, and Srivastava in their seminal work on the existence of infinite families of Ramanujan graphs.
ISSN: 0024-3795
DOI: 10.1016/j.laa.2018.12.004
Schools: School of Physical and Mathematical Sciences 
Rights: © 2018 Elsevier Inc. All rights reserved. This paper was published in Linear Algebra and its Applications and is made available with permission of Elsevier Inc.
Fulltext Permission: open
Fulltext Availability: With Fulltext
Appears in Collections:SPMS Journal Articles

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