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Research Article

The diameter of strong orientations of strong products of graphs

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Pages 945-958 | Received 06 Dec 2019, Published online: 01 May 2020

References

  • J. Bang-Jensen and G. Gutin, Digraphs: Theory, Algorithms and Applications, Springer, London, 2000.
  • V. Chvátal and C. Thomassen, Distances in orientations of graphs, J. Combin. Theory Ser. B 24 (1978), 61–75.
  • R. Hammack, W. Imrich, and S. Klavžar, Handbook of product graphs, Second edition, CRC Press, Boca Raton, FL, 2011.
  • I. Hrastnik Ladinek and S. Špacapan, The diameter of strong orientations of strong products of graphs, arXiv:1909.12022.
  • K.M. Koh and E.G. Tay, On optimal orientations of Cartesian products of even cycles and paths, Networks 30 (1997), 1–7.
  • K.M. Koh and E.G. Tay, Optimal orientations of products of paths and cycles, Discrete Appl. Math. 78 (1997), 163–174.
  • K.M. Koh and E.G. Tay, On optimal orientations of Cartesian products of graphs (I), Discrete Math. 190 (1998), 115–136.
  • K.M. Koh and E.G. Tay, On optimal orientations of Cartesian products of graphs (II): complete graphs and even cycles, Discrete Math. 211 (2000), 75–102.
  • K.M. Koh and E.G. Tay, On optimal orientations of Cartesian products of trees, Graphs Combin. 17 (2001), 79–97.
  • M. Knor, R. Škrekovski, and A. Tepeh, Orientations of graphs with maximum Wiener index, Discrete Appl. Math. 211 (2016), 121–129.
  • M. Knor, R. Škrekovski, and A. Tepeh Some remarks on the Wiener index of digraphs, Appl. Math. Comput. 273 (2016), 631–636.
  • T. Paj-Erker, Optimal orientations of strong products of paths, ADAM 2 (2019), #P1.04
  • I. Peterin and P. Žigert Pleteršek, Wiener index of strong product of graphs, Opuscula Math. 38(1) (2018), 81–94.
  • J. Plesník, On the sum of all distances in a graph or digraph, J. Graph Theory 8 (1984) 1–21.
  • H.E. Robbins, A theorem on graphs with an application to a problem on traffic control, Am. Math. Month. 46 (1939), 281–283.
  • F.S. Roberts and Y. Xu, On the optimal strongly connected orientations of city street graphs I: Large grids, SIAM J. Discrete Math. 1(2) (1988), 199–222.
  • F.S. Roberts and Y. Xu, On the optimal strongly connected orientations of city street graphs II: Two east-west avenues or north-south streets, Networks 19 (1989), 221– 233.
  • F.S. Roberts and Y. Xu, On the optimal strongly connected orientations of city street graphs III: Three east-west avenues or north-south streets, Networks 22 (1992), 109–143.
  • Y. Shitov, Counterexamples to Hedetniemi’s conjecture, arXiv:1905.02167v2.
  • S. Špacapan, The diameter of strong orientations of Cartesian products of graphs, Discrete Appl. Math. 247 (2018), 116–121.