A list of 4-valent 2-arc-transitive graphs and finite faithful amalgams of index (4,2)

An s-arc in a simple graph Gamma is an is (s + 1)-tuple of vertices of Gamma in which every two consecutive vertices are adjacent and every three consecutive vertices are pairwise distinct. A graph Gamma is said to be 2-arc-transitive if the automorphism group Aut(Gamma) acts transitively on the set of2-arcs of Gamma. It is shown that there are exactly 70 simple connected 2-arc-transitive 4-valent graphs oil no more than 512 vertices. A description of these graphs as coset graphs is given, and some basic graph theoretical properties are computed. The list is obtained by first determining all finite faithful amalgams of index (4, 2). and then using a computer implementation of a small index subgroups algorithm. (C) 2008 Elsevier Ltd. All rights reserved.