On Eulerian orientations of even-degree hypercubes

TL;DR

This paper proves that every Eulerian orientation of an even-degree hypercube maintains strong node connectivity proportional to its degree, extending known edge connectivity results to node connectivity.

Contribution

It establishes that all Eulerian orientations of even-degree hypercubes are strongly node connected, a novel extension of connectivity properties in graph orientations.

Findings

Eulerian orientations of hypercubes are strongly k-node connected

Extends known edge connectivity results to node connectivity

Provides new insights into hypercube orientation properties

Abstract

It is well known that \textit{every} Eulerian orientation of an Eulerian $2k$-edge connected (undirected) graph is strongly $k$-edge connected. An important goal in the area is to obtain analogous results for other types of connectivity, such as node connectivity and element connectivity. We show that \textit{every} Eulerian orientation of the hypercube of degree $2k$ is strongly $k$-node connected.