Öz
A dominating set of a graph G which intersects every independent set of a maximum cardinality in G is called an independent transversal dominating set. The minimum cardinality of an independent transversal dominating set is called the independent transversal domination number of G and is denoted by gamma_{it}(G). In this paper we investigate the independent transversal domination number of the path graph P_{n} with the star graph S_{1,m}, the wheel graph W_{1,m} and the complete graph K_{n} under neihgbourhood corona, edge corona and join operation providing \beta(P_{n})>\beta(G).
Anahtar Kelimeler
domination number independent transversal domination number independence number
Kaynakça
- 1)Ahangar H.A., Samodivkin V. and Yero I.G., Independent Transversal Dominating Sets in Graphs. Complexity and Structural Properties. Filomat. 30(2), 2016, 293--303.
- 2)Alon N., Fellows M.R. and Hare D.R., Vertex Transversals that Dominate. Journal of Graph Theory. 21(1), 1996, 21--31.
- 3)Brause C., Henning M., Ozeki K., Schiermeyer I. and Vumar E., On Upper Bounds For The Independent Transversal Domination Number. Discrete Applied Mathematics. Vol. 236, 2018, 66--72.
- 4)Chartrand G. and Lesniak L., Graphs and Digraphs, Fourth Edition, 2005.
- 5)Gopalapillai I., The spectrum of Neigbourhood Corona of Graphs. Kragujevac Journal of Mathematics. 35(3), 2011, 493--500.
- 6)Hamid I.S., Independent Transversal Domination ın Graphs. Discussiones Mathematicae Graph Theory. Vol.32, 2012, 5--7.
- 7)Harary F., Graph Theory, Addition-Wesley Publishing Co., Reading, MA/Menlo Park, CA/London, 1969.
- 8) Haynes T. W., Hedeniemi S. T. and Slater P. J., Fundamentals of Domination in Graphs, Marcel Dekker, Inc, New York, 1998.
- 9)Henning M.A., Domination in Graphs: a survey. Cong. Number., In G. Chartrand and M. Jacobson, editors, Surveys in Graph Theory. Vol. 116, 1996, 139--172.
- 10)Hou Y. and Shiu W., The spectrum of edge corona of graphs. Electronic Journal of Linear Algebra. Vol. 20, 2010, 586--594.
Öz
Kaynakça
- 1)Ahangar H.A., Samodivkin V. and Yero I.G., Independent Transversal Dominating Sets in Graphs. Complexity and Structural Properties. Filomat. 30(2), 2016, 293--303.
- 2)Alon N., Fellows M.R. and Hare D.R., Vertex Transversals that Dominate. Journal of Graph Theory. 21(1), 1996, 21--31.
- 3)Brause C., Henning M., Ozeki K., Schiermeyer I. and Vumar E., On Upper Bounds For The Independent Transversal Domination Number. Discrete Applied Mathematics. Vol. 236, 2018, 66--72.
- 4)Chartrand G. and Lesniak L., Graphs and Digraphs, Fourth Edition, 2005.
- 5)Gopalapillai I., The spectrum of Neigbourhood Corona of Graphs. Kragujevac Journal of Mathematics. 35(3), 2011, 493--500.
- 6)Hamid I.S., Independent Transversal Domination ın Graphs. Discussiones Mathematicae Graph Theory. Vol.32, 2012, 5--7.
- 7)Harary F., Graph Theory, Addition-Wesley Publishing Co., Reading, MA/Menlo Park, CA/London, 1969.
- 8) Haynes T. W., Hedeniemi S. T. and Slater P. J., Fundamentals of Domination in Graphs, Marcel Dekker, Inc, New York, 1998.
- 9)Henning M.A., Domination in Graphs: a survey. Cong. Number., In G. Chartrand and M. Jacobson, editors, Surveys in Graph Theory. Vol. 116, 1996, 139--172.
- 10)Hou Y. and Shiu W., The spectrum of edge corona of graphs. Electronic Journal of Linear Algebra. Vol. 20, 2010, 586--594.
Ayrıntılar
| Birincil Dil | İngilizce |
|---|---|
| Bölüm | Volume VII Issue I |
| Yazarlar | |
| Yayımlanma Tarihi | 30 Nisan 2022 |
| Yayımlandığı Sayı | Yıl 2022 Cilt: 7 Sayı: 1 |
