Three-arc graphs: Characterization and domination

An arc of a graph is an oriented edge and a 3-arc is a 4-tuple (v,u,x,y)(v,u,x,y) of vertices such that both (v,u,x)(v,u,x) and (u,x,y)(u,x,y) are paths of length two. The 3-arc graph of a graph GG is defined to have vertices the arcs of GG such that two arcs uv,xyuv,xy are adjacent if and only if (v,u,x,y)(v,u,x,y) is a 3-arc of GG. In this paper we give a characterization of 3-arc graphs and obtain sharp upper bounds on the domination number of the 3-arc graph of a graph GG in terms that of GG.