A study of 3-arc graphs Original Research Article

An arc of a graph is an oriented edge and a 3-arc is a 4-tuple image of vertices such that both image and image are paths of length two. The 3-arc graph of a graph image is defined to have the arcs of image as vertices such that two arcs image are adjacent if and only if image is a 3-arc of image. In this paper, we study the independence, domination and chromatic numbers of 3-arc graphs and obtain sharp lower and upper bounds for them. We introduce a new notion of arc-coloring of a graph in studying vertex-colorings of 3-arc graphs.