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Independent Transversal Domination Number of Corona and Join Operation in Path Graphs

Yıl 2022, Cilt: 7 Sayı: 1, 7 - 13, 30.04.2022

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).

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.
Yıl 2022, Cilt: 7 Sayı: 1, 7 - 13, 30.04.2022

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.
Toplam 10 adet kaynakça vardır.

Ayrıntılar

Birincil Dil İngilizce
Bölüm Volume VII Issue I
Yazarlar

Betül Atay Atakul 0000-0003-1964-3287

Yayımlanma Tarihi 30 Nisan 2022
Yayımlandığı Sayı Yıl 2022 Cilt: 7 Sayı: 1

Kaynak Göster

APA Atay Atakul, B. (2022). Independent Transversal Domination Number of Corona and Join Operation in Path Graphs. Turkish Journal of Science, 7(1), 7-13.
AMA Atay Atakul B. Independent Transversal Domination Number of Corona and Join Operation in Path Graphs. TJOS. Nisan 2022;7(1):7-13.
Chicago Atay Atakul, Betül. “Independent Transversal Domination Number of Corona and Join Operation in Path Graphs”. Turkish Journal of Science 7, sy. 1 (Nisan 2022): 7-13.
EndNote Atay Atakul B (01 Nisan 2022) Independent Transversal Domination Number of Corona and Join Operation in Path Graphs. Turkish Journal of Science 7 1 7–13.
IEEE B. Atay Atakul, “Independent Transversal Domination Number of Corona and Join Operation in Path Graphs”, TJOS, c. 7, sy. 1, ss. 7–13, 2022.
ISNAD Atay Atakul, Betül. “Independent Transversal Domination Number of Corona and Join Operation in Path Graphs”. Turkish Journal of Science 7/1 (Nisan 2022), 7-13.
JAMA Atay Atakul B. Independent Transversal Domination Number of Corona and Join Operation in Path Graphs. TJOS. 2022;7:7–13.
MLA Atay Atakul, Betül. “Independent Transversal Domination Number of Corona and Join Operation in Path Graphs”. Turkish Journal of Science, c. 7, sy. 1, 2022, ss. 7-13.
Vancouver Atay Atakul B. Independent Transversal Domination Number of Corona and Join Operation in Path Graphs. TJOS. 2022;7(1):7-13.