A note on symmetric graphs of valency eight

Abstract

A graph, with a group G of its automorphisms, is said to be (Gy s)-transitive, if G is transitive on s-arcs but not on (s + l)-arcs of the graph. Let A" be a connected (G, s)-transitive graph, and let Gv be the vertex stabilizer of a vertex t; V(X) in G. In this paper, we determine the structure of the vertex stabilizer Gv when X has valency eight and s >2. © 2019 Utilitas Mathematica Publishing Inc.. All rights reserved.