A note on the Weiss conjecture

TL;DR

This paper presents an alternative formulation of the Weiss Conjecture by relating vertex stabilizer bounds in finite group actions on graphs to the second singular value of a bipartite graph.

Contribution

It establishes an equivalence between bounding vertex stabilizer order and the second singular value, offering a new perspective on the Weiss Conjecture.

Findings

Bounding vertex stabilizer order is equivalent to bounding the second singular value.

Provides an alternative formulation of the Weiss Conjecture.

Links group action properties to spectral graph theory.

Abstract

Let $G$ be a finite group acting vertex-transitively on a graph. We show that bounding the order of a vertex stabilizer is equivalent to bounding the second singular value of a particular bipartite graph. This yields an alternative formulation of the Weiss Conjecture.