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Bibliographic Details
Main Author: Carter, Rebecca
Format: Preprint
Published: 2025
Subjects:
Online Access:https://arxiv.org/abs/2511.01738
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author Carter, Rebecca
author_facet Carter, Rebecca
contents We establish an Expander Mixing Lemma for directed graphs in terms of the eigenvalues of an associated asymmetric transition probability matrix, extending the classical spectral inequality to the asymmetric setting. As an application, we derive a spectral bound on the toughness of directed graphs that generalizes Alon's bound for $k$-regular graphs, showing how structural properties of directed graphs can be captured through their asymmetric spectra.
format Preprint
id arxiv_https___arxiv_org_abs_2511_01738
institution arXiv
publishDate 2025
record_format arxiv
spellingShingle Spectral Bounds for Directed Graphs Via Asymmetric Matrices: Applications to Toughness
Carter, Rebecca
Combinatorics
05C20 (Primary) 05C42 (Secondary)
We establish an Expander Mixing Lemma for directed graphs in terms of the eigenvalues of an associated asymmetric transition probability matrix, extending the classical spectral inequality to the asymmetric setting. As an application, we derive a spectral bound on the toughness of directed graphs that generalizes Alon's bound for $k$-regular graphs, showing how structural properties of directed graphs can be captured through their asymmetric spectra.
title Spectral Bounds for Directed Graphs Via Asymmetric Matrices: Applications to Toughness
topic Combinatorics
05C20 (Primary) 05C42 (Secondary)
url https://arxiv.org/abs/2511.01738