# Orientation distance graphs revisited

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

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## Abstract

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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.

## How to cite

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Wayne 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
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

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1. [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. [2] K. Kanakadandi, On Orientation Distance Graphs, M. Sc. thesis, (Clemson University, Clemson, 2006). Zbl1133.05040
3. [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. [4] B. McKay's Digraphs page, at: http://cs.anu.edu.au/∼bdm/data/digraphs.html.
5. [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. [6] B. Zelinka, The distance between various isomorphisms of a graph, Math. Slovaka 38 (1988) 19-25. Zbl0644.05024

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