On the stabilisers of locally 2-transitive graphs

Shu Jiao Song

paper

On the stabilisers of locally 2-transitive graphs

arXiv:1603.08398

Abstract

For a connected locally $(G, s$ )-arc-transitive graph $Γ$ with $s ⩾ 2$ and an edge $v, w$ , determining the amalgam $(G_{v}, G_{w}, G_{v w})$ is a fundamental problem in the area of symmetrical graph theory, but it is very difficult. In this paper, we give a classification of $(G_{v}, G_{w}, G_{v w})$ in the case where the vertex stabilisers $G_{v}$ and $G_{w}$ are faithful on their neighbourhoods, which shows that except for the case $G_{v} ≅ G_{w}$ , there are exactly 16 such triples.