Abstract. A 3-arc is 4-touple (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), has the vertex set identical with the set of arcs of G. Two arcs uv and xy are adjacent in X(G) if and only if (v,u,x,y) is a 3-arc in G. We study the diameter and connectivity of 3-arc graphs.

We prove that X(G) is connected if and only if minimum degree of G is at least 2 and G* is connected, where G* is obtained from G by splitting of every vertex of degree 2 into two vertices of degree 1. Further, we prove that if G has connectivity k, then X(G) has connectivity at least (k-1)2, the bound being the best possible. As regards the diameter, we prove that diam(X(G)) is bounded by diam(G) and diam(G)+2, the upper bound being valid if the minimum degree of G is at least 3. If the minimum degree of G is 2, then diam(X(G)) is unbounded from above if diam(G) is at least 4, and it is bounded by a constant if the diameter of G is at most 3.