Communications of the Korean Mathematical Society (대한수학회논문집)

Korean Mathematical Society (대한수학회)
권호 표지
DOI QR코드

DOI QR Code

THE HULL NUMBER OF POWERS OF CYCLES

  • Al-Ezeh, Hasan (Department of Mathematics School of Science The University of Jordan) ;
  • Ghanem, Manal (Department of Mathematics School of Science The University of Jordan) ;
  • Rwalah, Jameel (Department of Mathematics School of Science The University of Jordan)
  • Received : 2016.12.06
  • Accepted : 2017.06.14
  • Published : 2017.10.31
Download PDF
⟨ Previous Next ⟩

Abstract

Let $C_n$ be the cycle graph of order n on the vertices $v_0,v_1,{\ldots},v_n$ and $C^k_n$ be the k-th power of $C_n$. In this article we determine the hull-number of $C^k_n$.

Keywords

References

  1. O. AbuGhneim, B. Al-Khamaiseh, and H. Al-Ezeh, The geodetic, hull, and Steiner numbers of powers of paths, Util. Math. 95 (2014), 289-294.
  2. J. Bermond, F. Cormellas, and D. F. Hsu, Distributed loop computer networks: a survey, J. Parallel Distributed Computing 24 (1995), 2-10. https://doi.org/10.1006/jpdc.1995.1002
  3. J. Caceresa, C. Hernandob, M. Morab, I. M. Pelayob, and M. L. Puertasa, On the geodetic and the hull numbers in strong product graphs, Comput. Math. Appl. 60 (2010), no. 11, 3002-3031.
  4. S. R. Canoy, G. B. Cagaanan, and S. V. Gervacio, Convexity, geodetic and hull numbers of the join of graphs, Utilitas Math. 71 (2006), 143-159.
  5. G. Chartrand, J. F. Fink, and P. Zhang, Convexity in oriented graphs, Discrete Appl. Math. 116 (2002), 115-126. https://doi.org/10.1016/S0166-218X(00)00382-6
  6. G. Chartrand, J. F. Fink, and P. Zhang, The hull number of an oriented graph, International J. Math. Math. Sci. 36 (2003), 2265-2275.
  7. M. C. Dourado, J. G. Gimbel, J. Kratochvil, F. Protti, and J. L. Szwarc ter, On the computation of the hull number of a graph, Discrete Math. 309 (2009), no. 18, 5668- 5674. https://doi.org/10.1016/j.disc.2008.04.020
  8. M. G. Everett and S. B. Seidman, The hull number of a graph, Discrete Math. 57 (1985), no. 3, 217-223. https://doi.org/10.1016/0012-365X(85)90174-8
  9. M. Farber and R. E. Jamison, Convexity in graphs and hypergraphs, SIAM J. Algebraic Discrete Methods 7 (1986), no. 3, 433-444. https://doi.org/10.1137/0607049
  10. D. E. Knuth, The Art of Computer Programming. Vol. 3, Addison-Wesley, Reading, MA, 1975.