Three-arc graphs: characterization and domination

Abstract

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 graph $G$ is defined to have vertices the arcs of $G$ such that two arcs $uv, xy$ are adjacent if and only if $(v,u,x,y)$ is a 3-arc of $G$. 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 $G$ in terms that of $G$.