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2013 | 33 | 2 | 387-394
Tytuł artykułu

On the Domination of Cartesian Product of Directed Cycles: Results for Certain Equivalence Classes of Lengths

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EN
Abstrakty
EN
Let (−→ Cm2−→ Cn) be the domination number of the Cartesian product of directed cycles −→ Cm and −→ Cn for m, n ≥ 2. Shaheen [13] and Liu et al. ([11], [12]) determined the value of (−→ Cm2−→ Cn) when m ≤ 6 and [12] when both m and n ≡ 0(mod 3). In this article we give, in general, the value of (−→ Cm2−→ Cn) when m ≡ 2(mod 3) and improve the known lower bounds for most of the remaining cases. We also disprove the conjectured formula for the case m ≡ 0(mod 3) appearing in [12].
Wydawca
Rocznik
Tom
33
Numer
2
Strony
387-394
Opis fizyczny
Daty
wydano
2013-05-01
online
2013-04-13
Twórcy
Bibliografia
  • [1] T.Y. Chang and W.E. Clark, The domination numbers of the 5 × n and 6 × n grid graphs, J. Graph Theory 17 (1993) 81-107. doi:10.1002/jgt.3190170110[Crossref]
  • [2] M. El-Zahar and C.M. Pareek, Domination number of products of graphs, Ars Combin. 31 (1991) 223-227.
  • [3] M. El-Zahar, S. Khamis and Kh. Nazzal, On the domination number of the Cartesian product of the cycle of length n and any graph, Discrete Appl. Math. 155 (2007) 515-522. doi:10.1016/j.dam.2006.07.003[WoS][Crossref]
  • [4] R.J. Faudree and R.H. Schelp, The domination number for the product of graphs, Congr. Numer. 79 (1990) 29-33.
  • [5] S. Gravier and M. Mollard, On domination numbers of Cartesian product of paths, Discrete Appl. Math. 80 (1997) 247-250. doi:10.1016/S0166-218X(97)00091-7[Crossref]
  • [6] B. Hartnell and D. Rall, On dominating the Cartesian product of a graph and K2, Discuss. Math. Graph Theory 24 (2004) 389-402. doi:10.7151/dmgt.1238[Crossref]
  • [7] T.W. Haynes, S.T. Hedetniemi and P.J. Slater, Fundamentals of Domination in Graphs (Marcel Dekker, Inc. New York, 1998).
  • [8] T.W. Haynes, S.T. Hedetniemi and P.J. Slater, Domination in Graphs: Advanced Topics (Marcel Dekker, Inc. New York, 1998).
  • [9] M.S. Jacobson and L.F. Kinch, On the domination number of products of graphs I , Ars Combin. 18 (1983) 33-44.
  • [10] S. Klavžar and N. Seifter, Dominating Cartesian products of cycles, Discrete Appl. Math. 59 (1995) 129-136. doi:10.1016/0166-218X(93)E0167-W[Crossref]
  • [11] J. Liu, X.D. Zhang, X. Chenand and J. Meng, On domination number of Cartesian product of directed cycles, Inform. Process. Lett. 110 (2010) 171-173. doi:10.1016/j.ipl.2009.11.005[Crossref]
  • [12] J. Liu, X.D. Zhang, X. Chen and J. Meng, Domination number of Cartesian products of directed cycles, Inform. Process. Lett. 111 (2010) 36-39. doi:10.1016/j.ipl.2010.10.001[Crossref]
  • [13] R.S. Shaheen, Domination number of toroidal grid digraphs, Util. Math. 78 (2009) 175-184.
Typ dokumentu
Bibliografia
Identyfikatory
Identyfikator YADDA
bwmeta1.element.doi-10_7151_dmgt_1668
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