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 u v , x y 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 .

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