A study of 3-arc graphs

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 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. This is a preprint of an article accepted for publication in Discrete Applied Mathematics c 2011 (copyright owner as specified in the journal). Key words: 3-arc graph, domination number, independence number, chromatic number, arc coloring AMS subject classification (2000): 05C69, 05C15

• Type: Journal
• Year: 2011
• Where: DAM
• Authors: Martin Knor, Guangjun Xu, Sanming Zhou
• Keywords: 3-arc Graph, AMS Subject Classification, Chromatic Number, DAM 2011, Theoretical Computer Science