Maximal digraphs whose Hermitian spectral radius is at most $2$

TL;DR

This paper classifies the largest directed graphs with a Hermitian spectral radius not exceeding 2, providing a comprehensive understanding of their structure and spectral properties.

Contribution

It introduces a complete classification of maximal digraphs with Hermitian spectral radius at most 2, advancing spectral graph theory.

Findings

Complete classification of maximal digraphs with spectral radius ≤ 2

Identification of structural properties of these digraphs

Contribution to spectral graph theory and graph classification

Abstract

We classify maximal digraphs whose Hermitian spectral radius is at most $2$.