Discussiones Mathematicae Graph Theory 27(1) (2007) 125-136
doi: 10.7151/dmgt.1349

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ORIENTATION DISTANCE GRAPHS REVISITED

Wayne Goddard  and  Kiran Kanakadandi

Department of Computer Science
Clemson University
Clemson, SC 29634-1906, USA
e-mail: goddard@cs.clemson.edu

Abstract

The orientation distance graph Do(G) of a graph G is defined as the graph whose vertex set is the pair-wise non-isomorphic orientations of G, and two orientations are adjacent iff the reversal of one edge in one orientation produces the other. Orientation distance graphs was introduced by Chartrand et al. in 2001. We provide new results about orientation distance graphs and simpler proofs to existing results, especially with regards to the bipartiteness of orientation distance graphs and the representation of orientation distance graphs using hypercubes. We provide results concerning the orientation distance graphs of paths, cycles and other common graphs.

Keywords: orientation, distance graph, arc reversal.

2000 Mathematics Subject Classification: 05C20 (05C12, 05C62).

References

[1] G. Chartrand, D. Erwin, M. Raines and P. Zhang, Orientation distance graphs, J. Graph Theory 34 (2001) 230-241, doi: 10.1002/1097-0118(200104)36:4<230::AID-JGT1008>3.0.CO;2-#.
[2] K. Kanakadandi, On Orientation Distance Graphs, M. Sc. thesis, (Clemson University, Clemson, 2006).
[3] M. Livingston and Q.F. Stout, Embeddings in hypercubes, Math. Comput. Modelling 11 (1988) 222-227, doi: 10.1016/0895-7177(88)90486-4.
[4] B. McKay's Digraphs page, at: http://cs.anu.edu.au/∼bdm/data/digraphs.html.
[5] Jeb F. Willenbring at Sloane's ``The Online Encyclopedia of Integer Sequences'' located at: http://www.research.att.com/projects/OEIS?Anum=A053656.
[6] B. Zelinka, The distance between various isomorphisms of a graph, Math. Slovaka 38 (1988) 19-25.

Received 20 January 2006
Revised 17 October 2006