On the k -dominating number of Cartesian products of two paths

Antoaneta Klobučar

Mathematica Slovaca (2005)

  • Volume: 55, Issue: 2, page 141-154
  • ISSN: 0232-0525

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Klobučar, Antoaneta. "On the $k$-dominating number of Cartesian products of two paths." Mathematica Slovaca 55.2 (2005): 141-154. <http://eudml.org/doc/31680>.

@article{Klobučar2005,
author = {Klobučar, Antoaneta},
journal = {Mathematica Slovaca},
language = {eng},
number = {2},
pages = {141-154},
publisher = {Mathematical Institute of the Slovak Academy of Sciences},
title = {On the $k$-dominating number of Cartesian products of two paths},
url = {http://eudml.org/doc/31680},
volume = {55},
year = {2005},
}

TY - JOUR
AU - Klobučar, Antoaneta
TI - On the $k$-dominating number of Cartesian products of two paths
JO - Mathematica Slovaca
PY - 2005
PB - Mathematical Institute of the Slovak Academy of Sciences
VL - 55
IS - 2
SP - 141
EP - 154
LA - eng
UR - http://eudml.org/doc/31680
ER -

References

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  1. EL-ZAHAR M.-PAREEK C. M., Domination number of products of graphs, Ars Combin. 31 (1991), 223-227. (1991) Zbl0746.05067MR1110240
  2. FAUDREE R. J.-SCHELP R. H., The domination number for the product of graphs, Congr. Numer. 79 (1990), 29-33. (1990) Zbl0862.05060MR1140493
  3. GRAVIER S.-KHELLADI A., On the dominating number of cross product of graphs, Discrete Math. 145 (1995), 273-277. (1995) MR1356600
  4. HAYNES T.-HEDETNIEMI S. T.-SLATER P. J., Fundamentals of Domination in Graphs, Marcel Dekker, New York, 1998. (1998) Zbl0890.05002MR1605684
  5. JACOBSON M. S.-KINCH L. F., On the domination number of products of graphs I, Ars Combin. 18 (1983), 33-44. (1983) MR0823829
  6. JACOBSON M. S.-KINCH L. F., On the domination number of the products of graphs II: Trees, J. Graph Theory 10 (1986), 97-106. (1986) MR0830061
  7. JAENISCH C. F. de, Applications de l'Analyse Mathematique an Jenudes Echecs, Petrograd, 1862. 
  8. JHA P. K.-KLAVŽAR S., Independance and matching in direct-product graphs, Ars Combin. 50 (1998), 53-63. (1998) MR1670588
  9. JHA P. K.-KLAVŽAR S.-ZMAZEK B., Isomorphic components of Kronecker product of bipartite graphs, Discuss. Math. Graph Theory 17 (1997), 301-309. (1997) Zbl0906.05050MR1627967
  10. KLAVŽAR S.-SEIFTER N., Dominating Cartesian products of cycles, Discrete Appl. Math. 59 (1995), 129-136. (1995) Zbl0824.05037MR1330534
  11. KLAVŽAR S.-ZMAZEK B., On a Vizing-like conjecture for direct product graphs, Discrete Math. 156 (1996), 243-246. (1996) Zbl0856.05054MR1405022
  12. KLOBUČAR A., Domination numbers of cardinal products of graphs, Math. Slovaca 49 (1999), 387-402. (1999) MR1719684
  13. KLOBUČAR A., The domination numbers of the cardinal products P 6 □ P n , Math. Commun. 4 (1999), 241-250. (1999) 
  14. KLOBUČAR A.-SEIFTER N., K-dominating sets of the cardinal products of paths, Ars Combin. 55 (2000), 33-41. MR1755215
  15. KLOBUČAR A., K-dominating sets of P 2 k + 2 x P n and P m x P n , Ars Combin. 58 (2001), 279-288. MR1820208
  16. VIZING V. G., The Cartesian product of graphs, Vychisl. Sistemy 9 (1963), 30-43. (1963) MR0209178

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