Diameter and connectivity of 3-arc graphs

An arc of a graph is an oriented edge and a 3-arc is a 4-tuple (v, u, x, y) of vertices such that both (v, u, x) and (u, x, y) are paths of length two. The 3-arc graph of a given graph G, X(G), is defined to have vertices the arcs of G. Two arcs uv, xy are adjacent in X(G) if and only if (v, u, x, y) is a 3-arc of G. This notion was introduced in recent studies of arc-transitive graphs. In this paper we study diameter and connectivity of 3-arc graphs. In particular, we obtain sharp bounds for the diameter and connectivity of X(G) in terms of the corresponding invariant of G. This is a preprint of an article accepted for publication in Discrete Mathematics c ©2010 (copyright owner as specified in the fournal).