# Orientation distance graphs revisited

Wayne Goddard; Kiran Kanakadandi

Discussiones Mathematicae Graph Theory (2007)

- Volume: 27, Issue: 1, page 125-136
- ISSN: 2083-5892

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topWayne Goddard, and Kiran Kanakadandi. "Orientation distance graphs revisited." Discussiones Mathematicae Graph Theory 27.1 (2007): 125-136. <http://eudml.org/doc/270602>.

@article{WayneGoddard2007,

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.},

author = {Wayne Goddard, Kiran Kanakadandi},

journal = {Discussiones Mathematicae Graph Theory},

keywords = {orientation; distance graph; arc reversal; representation; paths; cycles},

language = {eng},

number = {1},

pages = {125-136},

title = {Orientation distance graphs revisited},

url = {http://eudml.org/doc/270602},

volume = {27},

year = {2007},

}

TY - JOUR

AU - Wayne Goddard

AU - Kiran Kanakadandi

TI - Orientation distance graphs revisited

JO - Discussiones Mathematicae Graph Theory

PY - 2007

VL - 27

IS - 1

SP - 125

EP - 136

AB - 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.

LA - eng

KW - orientation; distance graph; arc reversal; representation; paths; cycles

UR - http://eudml.org/doc/270602

ER -

## References

top- [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-# Zbl0988.05044
- [2] K. Kanakadandi, On Orientation Distance Graphs, M. Sc. thesis, (Clemson University, Clemson, 2006). Zbl1133.05040
- [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. Zbl0644.05024

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