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Total Domination Multisubdivision Number of a Graph

References [1] H. Aram, S.M. Sheikholeslami and O. Favaron, Domination subdivision number of trees, Discrete Math. 309 (2009) 622-628. doi:10.1016/j.disc.2007.12.085 [2] S. Benecke and C.M. Mynhardt, Trees with domination subdivision number one, Australas. J. Combin. 42 (2008) 201-209. [3] M. Dettlaff, J. Raczek and J. Topp, Domination subdivision and multisubdivision numbers of graphs, submitted. [4] O. Favaron, H. Karami and S.M. Sheikholeslami, Disproof of a conjecture on the subdivision

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The Domination Number of K3 n

References [1] T.Y. Chang, Domination number of grid graphs, Ph.D. Thesis, (Department of Mathematics, University of South Florida, 1992). [2] T.Y. Chang and W.E. Clark, The domination numbers of the 5 × n and 6 × n grid graphs, J. Graph Theory 17 (1993) 81-108. doi:10.1002/jgt.3190170110 [3] M.H. El-Zahar and R.S. Shaheen, On the domination number of the product of two cycles, Ars Combin. 84 (2007) 51-64. [4] M.H. El-Zahar and R.S. Shaheen, The domination number of C8 □Cn and C9 □Cn, J. Egyptian

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Bounds on the Locating Roman Domination Number in Trees

and N. Jafari Rad, Locating-total domination critical graphs , Australas. J. Combin. 45 (2009) 227–234. [9] X.G. Chen and M.Y. Sohn, Bounds on the locating-total domination number of a tree , Discrete Appl. Math. 159 (2011) 769–773. doi:10.1016/j.dam.2010.12.025 [10] E.J. Cockayne, Paul A. Dreyer Jr., S.M. Hedetniemi and S.T. Hedetniemi, Roman domination in graphs , Discrete Math. 278 (2004) 11–22. doi:10.1016/j.disc.2003.06.004 [11] F. Foucaud, M.A. Henning, C. Löwenstein and T. Sass, Locating-dominating sets in twin-free graphs

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New Bounds on the Signed Total Domination Number of Graphs

an extremal problem in graph theory, Math. Fiz. Lapok 48 (1941) 436-452. [9] D.B. West, Introduction to Graph Theory (Second Edition, Prentice Hall, USA, 2001). [10] B. Zelinka, Signed total domination number of a graph, Czechoslovak Math. J. 51 (2001) 225-229. doi:10.1023/A:1013782511179 [11] W. Zhao, H. Wang and G. Xu, Total k-domination number in graphs, Int. J. Pure Appl. Math. 35 (2007) 235-242.

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Bounds on the Signed Roman k-Domination Number of a Digraph

. Math. Graph Theory 3 (2010) 377-383. doi: /10.7151/dmgt.1500 [5] G. Hao and J. Qian, On the sum of out-domination number and in-domination number of digraphs, Ars Combin. 119 (2015) 331-337. [6] F. Harary, R.Z. Norman and D. Cartwright, Structural Models (Wiley, New York, 1965). [7] M.A. Henning and V. Naicker, Bounds on the disjunctive total domination number of a tree, Discuss. Math. Graph Theory 36 (2016) 153-171. doi: 10.7151/dmgt.1854 [8] M.A. Henning and L. Volkmann, Signed Roman k-domination in

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Hop Domination in Graphs-II

. [5] T.W. Haynes, S.T. Hedetniemi and P.J. Slater, Domination in Graphs - Advanced Topics, Marcel Dekker Inc., 1998. [6] T.W. Haynes, M.A. Henning and P.J. Slater, Strong equality of domination parameters in trees, Discrete Mathematics, 260:77-87,2003. [7] J.R. Lewis, Vertex-edge and Edge-vertex paramaters in graphs, PhD The- sis, Graduate School of Clemson University, August 2007. [8] N. Sridharan, V.S.A. Subramanian and M.D. Elias, Bounds on the dis- tance two-domination number of a graph, Graphs and Combinatorics

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On The Roman Domination Stable Graphs

.06.004 [4] A. Hansberg, N. Jafari Rad and L. Volkmann, Vertex and edge critical Roman domination in graphs, Util. Math. 92 (2013) 73-88. [5] T.W. Haynes, S.T. Hedetniemi and P.J. Slater, Fundamentals of Domination in Graphs (Marcel Dekker, Inc., New York, 1998). [6] N. Jafari Rad and L. Volkmann, Changing and unchanging the Roman domination number of a graph, Util. Math. 89 (2012) 79-95. [7] C.-H. Liu and G.J. Chang, Roman domination on strongly chordal graphs, J. Comb. Optim. 26 (2013) 608-619. doi: 10.1007/s10878

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A note on the k-tuple total domination number of a graph

References [1] G. Chang, The upper bound on k-tuple domination numbers of graphs , European Journal of Combinatorics 29 (2008) 1333-1336. [2] F. Harary, T. W. Haynes, Double domination in graphs , Ars Combin. 55 (2000) 201-213. [3] T. W. Haynes, S. T. Hedetniemi, P. J. Slater (eds). Fundamentals Domination in Graphs , Marcel Dekker, Inc. New York, 1998. [4] T. W. Haynes, S. T. Hedetniemi, P. J. Slater (eds), Domination in Graphs: Advanced Topics , Marcel Dekker, Inc. New York, 1998. [5] M. A. Henning, A survey of selected recent

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Domination Subdivision and Domination Multisubdivision Numbers of Graphs

R eferences [1] H. Aram, S.M. Sheikholeslami and O. Favaron, Domination subdivision numbers of trees , Discrete Math. 309 (2009) 622–628. doi:10.1016/j.disc.2007.12.085 [2] D. Avella-Alaminos, M. Dettlaff, M. Lemańska and R. Zuazua, Total domination multisubdivision number of a graph , Discuss. Math. Graph Theory 35 (2015) 315–327. doi:10.7151/dmgt.1798 [3] S. Benecke and C.M. Mynhardt, Trees with domination subdivision number one , Australas. J. Combin. 42 (2008) 201–209. [4] A. Bhattacharya and G.R. Vijayakumar, Effect of edge

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Fair Domination Number in Cactus Graphs

–148. [5] I.J. Dejter, Perfect domination in regular grid graphs , Australas. J. Combin. 42 (2008) 99–114. [6] I.J. Dejter and A.A. Delgado, Perfect domination in rectangular grid graphs , J. Combin. Math. Combin. Comput. 70 (2009) 177–196. [7] M.R. Fellows and M.N. Hoover, Perfect domination , Australas. J. Combin. 3 (1991) 141–150. [8] M. Hajian and N. Jafari Rad, Trees and unicyclic graphs with large fair domination number , Util. Math. accepted. [9] H. Hatami and P. Hatami, Perfect dominating sets in the Cartesian products of prime

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