×

Orientation distance graphs revisited. (English) Zbl 1133.05040

Summary: The orientation distance graph \({\mathcal D}_0(G)\) 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 G. Chartrand, D. Erwin, M. Raines, and P. Zhang [J. Graph Theory 36, No. 4, 230–241 (2001; Zbl 0988.05044)]. 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.

MSC:

05C20 Directed graphs (digraphs), tournaments
05C12 Distance in graphs
05C62 Graph representations (geometric and intersection representations, etc.)
05C38 Paths and cycles
05C45 Eulerian and Hamiltonian graphs

Citations:

Zbl 0988.05044
PDFBibTeX XMLCite
Full Text: DOI Link