3 papers
math.CO2026
All-to-all Routing on Kautz Graphs: Regular Routing Beats Shortest Paths
Vance Faber, Noah Streib
We study packet routing in the Kautz digraph K(d,D), where every ordered pair of distinct vertices is connected by a unique shortest directed path. The regular routing introduced i…
math.CO2025
Algebraic Constructions for the Digraph Routing Problems
Nyumbu Chishwashwa, Vance Faber, Noah Streib
Efficiency of routing on a regular digraph often involves finding opitmal properties of the graph. For example, the diameter of a digraph is the maximum distance between any two ve…
math.CO2025
All-to-all Routing on Digraph Networks
Nyumbu Chishwashwa, Vance Faber, Noah Streib
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…