Voir la notice de l'article provenant de la source Library of Science
@article{DMGT_2018_38_1_a4, author = {Varghese, Seethu and Vijayakumar, A. and Hinz, Andreas M.}, title = {Power {Domination} in {Kn\"odel} {Graphs} and {Hanoi} {Graphs}}, journal = {Discussiones Mathematicae. Graph Theory}, pages = {63--74}, publisher = {mathdoc}, volume = {38}, number = {1}, year = {2018}, language = {en}, url = {http://geodesic.mathdoc.fr/item/DMGT_2018_38_1_a4/} }
TY - JOUR AU - Varghese, Seethu AU - Vijayakumar, A. AU - Hinz, Andreas M. TI - Power Domination in Knödel Graphs and Hanoi Graphs JO - Discussiones Mathematicae. Graph Theory PY - 2018 SP - 63 EP - 74 VL - 38 IS - 1 PB - mathdoc UR - http://geodesic.mathdoc.fr/item/DMGT_2018_38_1_a4/ LA - en ID - DMGT_2018_38_1_a4 ER -
Varghese, Seethu; Vijayakumar, A.; Hinz, Andreas M. Power Domination in Knödel Graphs and Hanoi Graphs. Discussiones Mathematicae. Graph Theory, Tome 38 (2018) no. 1, pp. 63-74. http://geodesic.mathdoc.fr/item/DMGT_2018_38_1_a4/
[1] A. Aazami, Domination in graphs with bounded propagation: algorithms, formulations and hardness results, J. Comb. Optim. 19 (2010) 429–456. doi:10.1007/s10878-008-9176-7
[2] T.L. Baldwin, L. Mili, M.B. Boisen Jr. and R. Adapa, Power system observability with minimal phasor measurement placement, IEEE Trans. Power Systems 8 (1993) 707–715. doi:10.1109/59.260810
[3] J.-C. Bermond, H.A. Harutyunyan, A.L. Liestman and S. Perennes, A note on the dimensionality of modified Knödel graphs, Internat. J. Found. Comput. Sci. 8 (1997) 109–116. doi:10.1142/S0129054197000094
[4] G.J. Chang, P. Dorbec, M. Montassier and A. Raspaud, Generalized power domination of graphs, Discrete Appl. Math. 160 (2012) 1691–1698. doi:10.1016/j.dam.2012.03.007
[5] P. Dorbec, M.A. Henning, C. Löwenstein, M. Montassier and A. Raspaud, Generalized power domination in regular graphs, SIAM J. Discrete Math. 27 (2013) 1559–1574. doi:10.1137/120891356
[6] P. Dorbec and S. Klavžar, Generalized power domination: propagation radius and Sierpiński graphs, Acta Appl. Math. 134 (2014) 75–86. doi:10.1007/s10440-014-9870-7
[7] P. Dorbec, M. Mollard, S. Klavžar and S. Špacapan, Power domination in product graphs, SIAM J. Discrete Math. 22 (2008) 554–567. doi:10.1137/060661879
[8] M. Dorfling and M.A. Henning, A note on power domination in grid graphs, Discrete Appl. Math. 154 (2006) 1023–1027. doi:10.1016/j.dam.2005.08.006
[9] G. Fertin and A. Raspaud, A survey on Knödel graphs, Discrete Appl. Math. 137 (2004) 173–195. doi:10.1016/S0166-218X(03)00260-9
[10] T.W. Haynes, S.M. Hedetniemi, S.T. Hedetniemi and M.A. Henning, Domination in graphs applied to electric power networks, SIAM J. Discrete Math. 15 (2002) 519–529. doi:10.1137/S0895480100375831
[11] M.C. Heydemann, N. Marlin and S. Pérennes, Cayley graphs with complete rotations, Research Report INRIA 3624 (1999).
[12] A.M. Hinz, The Tower of Hanoi, Enseign. Math. (2) 35 (1989) 289–321.
[13] A.M. Hinz, S. Klavžar, U. Milutinović and C. Petr, The Tower of Hanoi—Myths and Maths (Springer, Basel, 2013).
[14] A.M. Hinz, S. Klavžar and S.S. Zemljič, A survey and classification of Sierpiński-type graphs, Discrete Appl. Math. 217 (2017) 565–600. doi:10.1016/j.dam.2016.09.024
[15] W. Knödel, New gossips and telephones, Discrete Math. 13 (1975) 95. doi:10.1016/0012-365X(75)90090-4
[16] F.T. Leighton, Introduction to Parallel Algorithms and Architectures: Arrays, Trees, Hypercubes (Morgan Kaufman, San Francisco CA, 1992).
[17] J.-H. Park and K.-Y. Chwa, Recursive circulant: a new topology for multicomputers networks, in: Proc. Int. Symp. Parallel Architectures, Algorithms and Networks (1994) 73–80. doi:10.1109/ISPAN.1994.367162
[18] S. Varghese and A. Vijayakumar, On the power domination number of graph products, Lecture Notes in Comput. Sci. 9602 (2016) 357–367. doi:10.1007/978-3-319-29221-2_31
[19] M. Zhao, L. Kang and G.J. Chang, Power domination in graphs, Discrete Math. 306 (2006) 1812–1816. doi:10.1016/j.disc.2006.03.037