All-to-all Routing on Digraph Networks

TL;DR

This paper explores the existence of spanning factorizations in vertex transitive digraphs, examining their properties and relationships to various graph structures, addressing an open problem in network routing theory.

Contribution

It investigates the open problem of whether all vertex transitive digraphs have spanning factorizations, analyzing related properties and their implications.

Findings

Relationships between vertex transitivity and spanning factorizations

Connections among cancellation, tree-like, and neighborhood preserving properties

Insights into the structure of regular digraphs for routing applications

Abstract

We discuss an open problem and its converse first posed by Dougherty and Faber in [3], "Network routing on regular directed graphs from spanning factorizations." Does every vertex transitive digraph have a spanning 1=factorization? We show relationships between various properties a regular digraph might have: vertex transitivity, left or right cancellation, tree-like or neighborhood preserving spanning factorizations.