# Minimum edge cuts of distance-regular and strongly regular digraphs

## TL;DR

This paper proves that in certain highly symmetric directed graphs, the minimum edge cuts are simple and correspond to edges incident to a single vertex, extending known undirected graph results.

## Contribution

It establishes that the edge connectivity equals the valency and characterizes minimum edge cuts in distance-regular and strongly regular digraphs, with new proofs.

## Key findings

- Edge connectivity equals valency k in these digraphs
- Minimum edge cuts are edges incident to a single vertex for k>2
- Results extend undirected graph properties to directed graphs

## Abstract

In this paper, we show that the edge connectivity of a distance-regular digraph $\Gamma$ with valency $k$ is $k$ and for $k>2$, any minimum edge cut of $\Gamma$ is the set of all edges going into (or coming out of) a single vertex. Moreover we show that the same result holds for strongly regular digraphs. These results extend the same known results for undirected case with quite different proofs.