Chartrand, Gary; Erwin, David; Raines, Michael; Zhang, Ping Orientation distance graphs. (English) Zbl 0988.05044 J. Graph Theory 36, No. 4, 230-241 (2001). The orientation distance between two orientations \(D\) and \(D'\) of a graph \(G\) is the minimum number of edges of \(G\) whose orientation needs to be reversed to transform \(D\) into an orientation isomorphic to \(D'\). The orientation distance graph with respect to \(G\) is a graph whose vertex set is a certain set of such orientations and in which two vertices are adjacent if and only if their orientation distance is one. If the vertex set is the set of all (pairwise non-isomorphic) orientations of \(G\), the orientation distance graph is denoted by \({\mathcal D}_0(G)\). The graph \({\mathcal D}_0(G)\) for \(G\) consisting of two non-isomorphic connected components is described. Further orientation distance graphs with respect to paths \(P_n\) with \(n\) vertices are studied. Every tree and every circuit is such a graph. If \(n\) is odd, then \({\mathcal D}_0(P_n)\) is bipartite. The graph \({\mathcal D}_0(P_n)\) for \(n\geq 4\) is Hamiltonian if and only if \(n\) is even. Reviewer: Bohdan Zelinka (Liberec) Cited in 1 Review MSC: 05C20 Directed graphs (digraphs), tournaments 05C62 Graph representations (geometric and intersection representations, etc.) 05C45 Eulerian and Hamiltonian graphs 05C12 Distance in graphs 05C38 Paths and cycles Keywords:orientation distance PDFBibTeX XMLCite \textit{G. Chartrand} et al., J. Graph Theory 36, No. 4, 230--241 (2001; Zbl 0988.05044) References: [1] Alavi, J Combin Inform System Sci 16 pp 1– (1991) · doi:10.1016/0306-4379(91)90045-B [2] and Metrics defined on spaces of graphs: a survey. (preprint). [3] Generalized Distance in Graphs. Ph.D. Dissertation, Western Michigan University (1988). [4] n-Tuple Vertex Graphs. M.S. Thesis, Emory University (1992). [5] Zelinka, Math Slovaca 38 pp 19– (1998) This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.