Spectral bound for separations in Eulerian digraphs

TL;DR

This paper establishes spectral bounds on the size of separations in Eulerian digraphs by analyzing the eigenvalues of their Laplacian matrices, advancing understanding of digraph spectra.

Contribution

It provides the first spectral bound on separations specifically for Eulerian digraphs, linking eigenvalues to structural properties.

Findings

Spectral bounds relate separation size to Laplacian eigenvalues.

The results apply to a subclass of Eulerian digraphs.

Advances spectral graph theory for directed graphs.

Abstract

The spectra of digraphs, unlike those of graphs, is a relatively unexplored territory. In a digraph, a separation is a pair of sets of vertices X and Y such that there are no arcs from X and Y . For a subclass of eulerian digraphs, we give an bound on the size of a separation in terms of the eigenvalues of the Laplacian matrix.