On the conjecture of vertex-transitivity of Dcell

TL;DR

This paper investigates the vertex-transitivity of Dcell networks, confirming the conjecture for small parameters and disproving it for larger ones, thus clarifying the symmetry properties of these data center topologies.

Contribution

It proves that Dcell networks are vertex-transitive for k ≤ 1 and not for k ≥ 2, resolving a conjecture about their symmetry.

Findings

Dcell is vertex-transitive for k ≤ 1 and n ≥ 2.

Dcell is not vertex-transitive for k ≥ 2 and n ≥ 2.

Clarifies the symmetry properties of Dcell networks.

Abstract

Gu et al. in [Inform. Process. Lett. 134 (2018) 52--56] conjectured that the data center network $D_{k,n}$ is vertex-transitive for all $k\geq0$ and $n\geq2$. In this paper, we show that $D_{k,n}$ is vertex-transitive for $k\leq1$ and $n\geq2$, and it is not vertex-transitive for all $k\geq2$ and $n\geq2$.