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Original Articles

Strong metric dimension of rooted product graphs

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Pages 1265-1280 | Received 09 Feb 2013, Accepted 09 Jun 2015, Published online: 06 Jul 2015

References

  • N. Biggs, Algebraic Graph Theory, 2nd ed., Cambridge University Press, Cambridge, 1993.
  • R.C. Brigham, G. Chartrand, R.D. Dutton, and P. Zhang, Resolving domination in graphs, Math. Bohemica 128(1) (2003), pp. 25–36.
  • A.E. Brouwer, A.M. Cohen, and A. Neumaier, Distance-Regular Graphs, Springer, Berlin, 1989.
  • J. Cáceres, C. Hernando, M. Mora, I.M. Pelayo, M.L. Puertas, C. Seara, and D.R. Wood, On the metric dimension of Cartesian product of graphs, SIAM J. Discret. Math. 21(2) (2007), pp. 273–302. doi: 10.1137/050641867
  • G. Chappell, J. Gimbel, and C. Hartman, Bounds on the metric and partition dimensions of a graph, Ars Combinatoria 88 (2008), pp. 349–366.
  • G. Chartrand, L. Eroh, M.A. Johnson, and O.R. Oellermann, Resolvability in graphs and the metric dimension of a graph, Discret. Appl. Math. 105 (2000), pp. 99–113. doi: 10.1016/S0166-218X(00)00198-0
  • G. Chartrand, C. Poisson, and P. Zhang, Resolvability and the upper dimension of graphs, Comput. Math. Appl. 39 (2000), pp. 19–28. doi: 10.1016/S0898-1221(00)00126-7
  • G. Chartrand, E. Salehi, and P. Zhang, The partition dimension of a graph, Aequationes Math. 59(1–2) (2000), pp. 45–54. doi: 10.1007/PL00000127
  • M. Fehr, S. Gosselin, and O.R. Oellermann, The partition dimension of Cayley digraphs, Aequationes Math. 71 (2006), pp. 1–18. doi: 10.1007/s00010-005-2800-z
  • M. Feng and K. Wang, On the metric dimension and fractional metric dimension of the hierarchical product of graphs, Appl. Anal. Discret. Math. 7(2) (2013), pp. 302–313. doi: 10.2298/AADM130521009F
  • C.D. Godsil and B.D. McKay, A new graph product and its spectrum, Bull. Aust. Math. Soc. 18(1) (1978), pp. 21–28. doi: 10.1017/S0004972700007760
  • F. Harary and R.A. Melter, On the metric dimension of a graph, Ars Combin. 2 (1976), pp. 191–195.
  • T.W. Haynes, M.A. Henning, and J. Howard, Locating and total dominating sets in trees, Discret. Appl. Math. 154 (2006), pp. 1293–1300. doi: 10.1016/j.dam.2006.01.002
  • M.A. Johnson, Structure-activity maps for visualizing the graph variables arising in drug design, J. Biopharm. Stat. 3 (1993), pp. 203–236. doi: 10.1080/10543409308835060
  • M.A. Johnson, Browsable structure-activity datasets, in Advances in Molecular Similarity, R. Carbó–Dorca and P. Mezey, eds., JAI Press, Connecticut, 1998, pp. 153–170.
  • S. Khuller, B. Raghavachari, and A. Rosenfeld, Landmarks in graphs, Discret. Appl. Math. 70 (1996), pp. 217–229. doi: 10.1016/0166-218X(95)00106-2
  • D. Kuziak, J.A. Rodríguez-Velázquez, and I.G. Yero, Computing the metric dimension of a graph from primary subgraphs. Submitted for publication.
  • D. Kuziak, I.G. Yero, and J.A. Rodríguez-Velázquez, Strong metric dimension of corona product graphs and join graphs, Discret. Appl. Math. 161(7/8) (2013), pp. 1022–1027. doi: 10.1016/j.dam.2012.10.009
  • T.R. May and O.R. Oellermann, The strong dimension of distance-hereditary graphs, J. Comb. Math. Comb. Comput. 76 (2011), pp. 59–73.
  • R.A. Melter and I. Tomescu, Metric bases in digital geometry, Comput. Vision Graph. Image Process. 25 (1984), pp. 113–121. doi: 10.1016/0734-189X(84)90051-3
  • O.R. Oellermann and J. Peters-Fransen, The strong metric dimension of graphs and digraphs, Discret. Appl. Math. 155 (2007), pp. 356–364. doi: 10.1016/j.dam.2006.06.009
  • F. Okamoto, B. Phinezyn, and P. Zhang, The local metric dimension of a graph, Math. Bohem. 135(3) (2010), pp. 239–255.
  • J.A. Rodríguez-Velázquez, I.G. Yero, D. Kuziak, and O.R. Oellermann, On the strong metric dimension of Cartesian and direct products of graphs, Discret. Math. 335 (2014), pp. 8–19. doi: 10.1016/j.disc.2014.06.023
  • V. Saenpholphat, and P. Zhang, Conditional resolvability in graphs: a survey, Int. J. Math. Math. Sci. 38 (2004), pp. 1997–2017. doi: 10.1155/S0161171204311403
  • A.J. Schwenk, Computing the characteristic polynomial of a graph, in Graphs and Combinatorics, R. Bari and F. Harary, eds., Springer, Berlin, 1974, pp. 153–172.
  • A. Sebö and E. Tannier, On metric generators of graphs, Math. Oper. Res. 29(2) (2004), pp. 383–393. doi: 10.1287/moor.1030.0070
  • P. J. Slater, Leaves of trees, Proceeding of the 6th Southeastern Conference on Combinatorics, Graph Theory, and Computing, Congr. Numer. 14 (1975), pp. 549–559.
  • P.J. Slater, Dominating and reference sets in a graph, J. Math. Phys. Sci. 22(4) (1988), pp. 445–455.
  • I. Tomescu, Discrepancies between metric and partition dimension of a connected graph, Discret. Math. 308 (2008), pp. 5026–5031. doi: 10.1016/j.disc.2007.08.089
  • I.G. Yero and J.A. Rodríguez-Velázquez, A note on the partition dimension of Cartesian product graphs, Appl. Math. Comput. 217(7) (2010), pp. 3571–3574. doi: 10.1016/j.amc.2010.08.038
  • I.G. Yero, D. Kuziak, and J.A. Rodríguez-Velázquez, On the metric dimension of corona product graphs, Comput. Math. Appl. 61(9) (2011), pp. 2793–2798. doi: 10.1016/j.camwa.2011.03.046

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