On the stabilisers of locally 2-transitive graphs

2016/03/28 by Shu Jiao Song, Song, Shu Jiao
Computer Science · Engineering · Mathematics · #Advanced Graph Theory Research #Combinatorics (math.CO) #FOS: Mathematics #Finite Group Theory Research #graph theory and CDMA systems

paper · pdf · doi:10.48550/arxiv.1603.08398

openalex publication_date 2016/03/28 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

For a connected locally (G,s)-arc-transitive graph Γ with s\geqslant 2 and an edge v,w, determining the amalgam (G_v,G_w,G_vw) 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_vw) 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.

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