A study of 3-arc graphs

Authors:
Martin Knor;Guangjun Xu;Sanming Zhou
Affiliations:
Department of Mathematics, Faculty of Civil Engineering, Slovak University of Technology, Radlinského 11, 813 68 Bratislava, Slovakia;Department of Mathematics and Statistics, The University of Melbourne, Parkville, VIC 3010, Australia;Department of Mathematics and Statistics, The University of Melbourne, Parkville, VIC 3010, Australia
Venue:
Discrete Applied Mathematics
Year:
2011

Citing 7
Cited 1

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Constructing a class of symmetric graphs

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Almost Covers Of 2-Arc Transitive Graphs

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Finite symmetric graphs with two-arc transitive quotients

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Finite symmetric graphs with two-arc transitive quotients II

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On the oriented chromatic index of oriented graphs

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Arc-chromatic number of digraphs in which every vertex has bounded outdegree or bounded indegree

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On the connectivity and restricted edge-connectivity of 3-arc graphs

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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 the arcs of G as vertices 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.