Über symmetrische Graphen vom grad fünf

Let G be a connected 1-transitive graph of valency five. It is shown that the order of a vertex stabilizer divides 5 · 3² · 2¹⁷. A theorem of A. Gardiner bounding the order of a vertex stabilizer of a 2-transitive graph of valency 1 + p,p prime, is reproved.