Voir la notice de l'article provenant de la source Library of Science
@article{DMGT_2015_35_4_a15, author = {Seo, Suk J. and Slater, Peter J.}, title = {Fault {Tolerant} {Detectors} for {Distinguishing} {Sets} in {Graphs}}, journal = {Discussiones Mathematicae. Graph Theory}, pages = {797--818}, publisher = {mathdoc}, volume = {35}, number = {4}, year = {2015}, language = {en}, url = {http://geodesic.mathdoc.fr/item/DMGT_2015_35_4_a15/} }
TY - JOUR AU - Seo, Suk J. AU - Slater, Peter J. TI - Fault Tolerant Detectors for Distinguishing Sets in Graphs JO - Discussiones Mathematicae. Graph Theory PY - 2015 SP - 797 EP - 818 VL - 35 IS - 4 PB - mathdoc UR - http://geodesic.mathdoc.fr/item/DMGT_2015_35_4_a15/ LA - en ID - DMGT_2015_35_4_a15 ER -
Seo, Suk J.; Slater, Peter J. Fault Tolerant Detectors for Distinguishing Sets in Graphs. Discussiones Mathematicae. Graph Theory, Tome 35 (2015) no. 4, pp. 797-818. http://geodesic.mathdoc.fr/item/DMGT_2015_35_4_a15/
[1] Y. Ben-Haim and S. Litsyn, Exact minimum density of codes identifying vertices in the square grid, SIAM J. Discrete Math. 19 (2005) 69-82. doi:10.1137/S0895480104444089
[2] N. Bertrand, I. Charon, O. Hudry and A. Lobstein, Identifying and locating- dominating codes on chains and cycles, European J. Combin. 25 (2004) 969-987. doi:10.1016/j.ejc.2003.12.013
[3] M. Blidia, M. Chellali, R. Lounes and F. Maffray, Characterizations of trees with unique minimum locating-dominating sets, J. Combin. Math. Combin. Comput. 76 (2011) 225-232.
[4] M. Blidia, M. Chellali, F. Maffray, J. Moncel and A. Semri, Locating-domination and identifying codes in trees, Australas. J. Combin. 39 (2007) 219-232.
[5] M. Chellali, N.J. Rad, S.J. Seo and P.J. Slater, On open neighborhood locating- dominating in graphs, Electron. J. Graph Theory Appl. 2 (2014) 87-98. doi:10.5614/ejgta.2014.2.2.1
[6] G.D. Cohen, I. Honkala, A. Lobstein and G. Zémor, Bounds for codes identifying vertices in the hexagonal grid, SIAM J. Discrete Math. 13 (2000) 492-504. doi:10.1137/S0895480199360990
[7] A. Cukierman and G. Yu, New bounds on the minimum density of an identifying code for the infinite hexagonal grid, Discrete Appl. Math. 161 (2013) 2910-2924. doi:10.1016/j.dam.2013.06.002
[8] G. Exoo, V. Junnila and T. Laihonen, Locating-dominating codes in cycles, Aus- tralas. J. Combin. 49 (2011) 177-194.
[9] F. Foucaud, R. Klasing and P.J. Slater, Centroidal bases in graphs, Networks 64 (2014) 96-108. doi:10.1002/net.21560
[10] D.L. Grinstead and P.J. Slater, Fractional domination and fractional packing in graphs, Congr. Numer. 71 (1990) 153-172.
[11] F. Harary and R. Melter, On the metric dimension of a graph, Ars Combin. 2 (1976) 191-195.
[12] T.W. Haynes, C. Sterling and P.J. Slater, Liar’s domination in ladders, Congr. Numer. 212 (2012) 45-56.
[13] M. Henning and A. Yeo, Distinguishing-transversal in hypergraphs and identifying open codes in cubic graphs, Graphs Combin. 30 (2014) 909-932. doi:10.1007/s00373-013-1311-2
[14] C. Hernando, M. Mora and I.M. Pelayo, Nordhaus-Gaddum bounds for locating domination, European J. Combin. 36 (2014) 1-6. doi:10.1016/j.ejc.2013.04.009
[15] C. Hernando, M. Mora, P.J. Slater and D.R. Wood, Fault-tolerant metric dimension of graphs, Ramanujan Math. Soc. Lect. Notes 5 (2008) 81-85.
[16] I. Honkala, An optimal locating-dominating set in the infinite triangular grid, Dis- crete Math. 306 (2006) 2670-2681. doi:10.1016/j.disc.2006.04.028
[17] I. Honkala, An optimal strongly identifying code in the infinite triangular grid, Elec- tron. J. Combin. 17 (2010) R91.
[18] I. Honkala and T. Laihonen, On locating-domination sets in infinite grids, European J. Combin. 27 (2006) 218-227. doi:10.1016/j.ejc.2004.09.002
[19] I. Honkala and T. Laihonen, On identifying codes that are robust against edge changes, Inform. and Comput. 205 (2007) 1078-1095. doi:10.1016/j.ic.2007.01.003
[20] I. Honkala, T. Laihonen and S. Ranto, On strongly identifying codes, Discrete Math. 254 (2002) 191-205. doi:10.1016/S0012-365X(01)00357-0
[21] M.G. Karpovsky, K. Chakrabarty and L.B. Levitin, On a new class of codes for identifying vertices in graphs, IEEE Trans. Inform. Theory 44 (1998) 599-611. doi:10.1109/18.661507
[22] R. Kincaid, A. Oldham and G. Yu, On optimal open locating-dominating sets in infinite triangular grids, March 28 (2014) manuscript. math.CO arXiv:1403.7061v1
[23] A. Lobstein, Watching systems, identifying, locating-dominating and discriminating codes in graphs. http://www.infres.enst.fr/lobstein/debutBIBidetlocdom.pdf
[24] J. Moncel, On graphs on n vertices having an identifying code of cardinality ⌈log2(n+ 1)⌉, Discrete Appl. Math. 154 (2006) 2032-2039. doi:10.1016/j.dam.2006.03.011
[25] B.S. Panda and S. Paul, A linear time algorithm for liar’s domination problem in proper interval graphs, Inform. Process. Lett. 113 (2013) 815-822. doi:10.1016/j.ipl.2013.07.012
[26] B.S. Panda and S. Paul, Hardness results and approximation algorithm for total liar’s domination in graphs, J. Comb. Optim. 27 (2014) 643-662. doi:10.1007/s10878-012-9542-3
[27] M.L. Roden and P.J. Slater, Liars’ domination and the domination continuum, Congr. Numer. 190 (2008) 77-85.
[28] M.L. Roden and P.J. Slater, Liar’s domination in graphs, Discrete Math. 309 (2009) 5884-5890. doi:10.1016/j.disc.2008.07.019
[29] M. Roden-Bowie and P.J. Slater, Set-sized (1, 3)-domination for trees, Congr. Nu- mer. 196 (2009) 203-213.
[30] S.J. Seo and P.J. Slater, Open neighborhood locating-dominating sets, Australas. J. Combin. 46 (2010) 109-120.
[31] S.J. Seo and P.J. Slater, Open neighborhood locating-dominating in trees, Discrete Appl. Math. 159 (2011) 484-489. doi:10.1016/j.dam.2010.12.010
[32] S.J. Seo and P.J. Slater, Open neighborhood locating-domination for infinite cylin- ders, Proceedings of ACM SE (2011) 334-335. doi:10.1145/2016039.2016134
[33] S.J. Seo and P.J. Slater, Open neighborhood locating-domination for grid-like graphs, Bull. Inst. Combin. Appl. 65 (2012) 89-100.
[34] S.J. Seo and P.J. Slater,Graphical parameters for classes of tumbling block graphs, Congr. Numer. 213 (2012) 155-168.
[35] S.J. Seo and P.J. Slater, Open locating-dominating interpolation for trees, Congr. Numer. 215 (2013) 145-152.
[36] S.J. Seo and P.J. Slater, Old trees with maximum degree three, Util. Math. 94 (2014) 361-380.
[37] J.L. Sewell, Ph.D. Dissertation, in preparation.
[38] J.L. Sewell and P.J. Slater, Fault tolerant identifying codes and locating-dominating sets, in preparation.
[39] P.J. Slater, Leaves of trees, Congr. Numer. 14 (1975) 549-559.
[40] P.J. Slater, Domination and location in graphs, National University of Singapore, Research Report 93 (1983).
[41] P.J. Slater, Dominating and location in acyclic graphs, Networks 17 (1987) 55-64. doi:10.1002/net.3230170105
[42] P.J. Slater, Dominating and reference sets in graphs, J. Math. Phys. Sci. 22 (1988) 445-455.
[43] P.J. Slater, Locating dominating sets and locating-dominating sets, in: Graph The- ory, Combinatorics, and Applications: Proceedings of the 7th Quadrennial International Conference on the Theory and Applications of Graphs 2 (1995) 1073-1079.
[44] P.J. Slater, Fault-tolerant locating-dominating sets, Discrete Math. 249 (2002) 179-189. doi:10.1016/S0012-365X(01)00244-8
[45] P.J. Slater, Liar’s domination, Networks 54 (2009) 70-74. doi:10.1002/net.20295
[46] P.J. Slater, A framework for faults in detectors within network monitoring systems, WSEAS Trans. Math. 12 (2013) 911-916.