Interlacing families and the Hermitian spectral norm of digraphs

• Main Authors: Greaves, Gary Royden Watson, Mohar, Bojan, O, Suil
• Other Authors: School of Physical and Mathematical Sciences
• Format: Article
• Language: English
• Published: 2021
• Subjects: Science::Mathematics; Hermitian Adjacency Matrix; Digraph
• Online Access: https://hdl.handle.net/10356/146676
• Institution: Nanyang Technological University

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 resolv...