Honam Mathematical Journal (호남수학학술지)

The Honam Mathematical Society (호남수학회)
권호 표지
DOI QR코드

DOI QR Code

INDEPENDENT TRANSVERSAL DOMINATION NUMBER IN COMPLEMENTARY PRISMS

  • Aytac, Aysun (Department of Mathematics, Faculty of Science, Ege University) ;
  • Erkal, Cem (Department of Mathematics, Faculty of Science, Ege University)
  • Received : 2020.07.09
  • Accepted : 2020.11.19
  • Published : 2021.03.25
Download PDF
⟨ Previous Next ⟩

Abstract

A set D ⊆ V (G) is an independent transversal dominating set of G if D is a dominating set and also intersects every maximum independent set in G. The minimum cardinality of such a set is equal to the transversal domination number, denoted by ��it(G). This paper is devoted to the computation of the independent transversal domination number of some complementary prism.

Keywords

References

  1. H. A. Ahangar, V. Samodivkin and I. G. Yero, Independent transversal dominating sets in graphs: complexity and structural properties, Filomat, 30(2) (2016), 293-303. https://doi.org/10.2298/FIL1602293A
  2. A. I. Alhashim, Roman Domination in Complementary Prisms, Master Thesis, East Tennessee State University, (2017).
  3. N. Alon, M. R. Fellows and D. R. Hare, Vertex transversals that dominate J. Graph Theory, 21(1) (1996), 21-31. https://doi.org/10.1002/(SICI)1097-0118(199601)21:1<21::AID-JGT3>3.0.CO;2-O
  4. A. Aytac and Z. Kartal, Total influence number in complementary prisms, Journal of the international Math. Virtual Inst., 9(2) (2019), 241-258.
  5. A. Aytac and T. Turaci, Strong Weak Domination in Complementary Prisms, Dynamics of Continuous, Discrete & Impulsive Systems Series B: Applications & Algorithms., 22 (2015), 85-96.
  6. J. A. Bond and U. S. R. Murty, Graph Theory, Springer, 2008.
  7. W. Goddard and M. A. Henning, Independent domination in graphs: A survey and recent results, Discrete Math., 313(7) (2013), 839-854. https://doi.org/10.1016/j.disc.2012.11.031
  8. J. Gongora, T. W. Haynes and E. Jum, Independent domination numbers in complementary prisms, Utilitas Mathematica, 91 (2013), 3-12.
  9. J. Gongora, Independent domination numbers in complementary prisms, Master Thesis, East Tennessee State University, 2009.
  10. M. R. Fellows, Transversals of vertex partitions in graphs, SIAM J. Discrete Math., 3(2) (1990), 206-215. https://doi.org/10.1137/0403018
  11. I. S. Hamid Independent transversal domination in graphs, Discuss. Math. Graph Theory, 32(1) (2012), 5-17. https://doi.org/10.7151/dmgt.1581
  12. T. W. Haynes, M. A Henning, P. J. Slater and L. C. Van der Merwe, The complementary product of two graphs, Bull Inst Comb Appl., 51 (2007), 21-30.
  13. T. W. Haynes, S. T. Hedetniemi and P.J. Slater, Fundamentals of domination in graphs, Marcel Dekker, New York, 1998.
  14. T. W. Haynes, S. T. Hedetniemi and L. C. Van der Merwe, Domination and total domination in complementary prisms, Bull Inst Comb Appl., 18 (2009), 23-37.
  15. M. A. Henning and A. Yeo, Total domination in graphs, Springer Monographs in Mathematics, Springer, New York, 2013.
  16. M. A. Henning, A survey of selected recent results on total domination in graphs, Discrete Mathematics, 309(1) (2009) 32-63. https://doi.org/10.1016/j.disc.2007.12.044
  17. K. R. S. Holmes, Locating-Domination in Complementary Prisms, Master Thesis, East Tennessee State University, (2009).
  18. A. P. Kazemi, k-tuple total domination number of the complementary prism, International Scholarly Research Network ISRN Discrete Mathematics, doi:10.5402/2011/681274, (2011), 1-13.
  19. D. A. Mojdeh, A. Parsian and I. Masoumi, Strong Roman Domination Number of Complementary Prism Graphs Turk. J. Math. Comput. Sci., 11(1) (2019) 40-47.
  20. H. D. Russell, Italian Domination in Complementary Prisms, Master Thesis, East Tennessee State University, (2018).