Geodesic
Orientation distance graphs revisited
Discussiones Mathematicae. Graph Theory, Tome 27 (2007) no. 1, pp. 125-136.

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The orientation distance graph ₒ(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 
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Goddard, Wayne; Kanakadandi, Kiran. Orientation distance graphs revisited. Discussiones Mathematicae. Graph Theory, Tome 27 (2007) no. 1, pp. 125-136. http://geodesic.mathdoc.fr/item/DMGT_2007_27_1_a10/

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