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On Domination Polynomials of Caterpillar Graphs

Year 2018, Volume: 9, 34 - 38, 28.12.2018

Abstract

The domination polynomial of a simple graph  is calculated with  such that   is the number of the
dominating sets of G of size
. In this paper we study the domination polynomials of caterpillar
graphs.

References

  • Alikhani, S., Peng, Y.H., Dominating sets and domination polynomial of cycles, Global Journal of Pure and Applied Mathematics, 4(2)(2008), 151–162.
  • Alikhani, S., Peng, Y.H., Domination polynomials of cubic graphs of order 10, Turk. J. Math., 35(3)(2011), 355–366.
  • Alikhani, S., Peng, Y.H., Introduction to domination polynomial of a graph, Ars Combin., 114(2014), 257–266.
  • Gutman, I., Some analytic properties of the independence and matching polynomials, Match., 28(1992), 139–150.
  • Haynes, T.W., Hedetniemi, S.T., Slater, P.J., Fundamentals of Domination in Graphs, Marcel Dekker, New York, 1998.
  • Klavzar, S., Mollard, M., Wiener index and Hosoya polynomial of Fibonacci and Lucas qubes, MATCH Commun. Math. Comput. Chem., 68(2012), 311–324.
  • Majstorovic, S., Doslic, T., Klobucar, A., k-domination on hexagonal cactus chains, Kragujevac Journal of Mathematics, 2(2012), 335–347.
  • Vukicevic, D., Klobucar A., k-dominating sets on linear benzenoids and on the infinite hexagonal grid, Croatica Chemica Acta, 80(2)(2007), 187–191.
Year 2018, Volume: 9, 34 - 38, 28.12.2018

Abstract

References

  • Alikhani, S., Peng, Y.H., Dominating sets and domination polynomial of cycles, Global Journal of Pure and Applied Mathematics, 4(2)(2008), 151–162.
  • Alikhani, S., Peng, Y.H., Domination polynomials of cubic graphs of order 10, Turk. J. Math., 35(3)(2011), 355–366.
  • Alikhani, S., Peng, Y.H., Introduction to domination polynomial of a graph, Ars Combin., 114(2014), 257–266.
  • Gutman, I., Some analytic properties of the independence and matching polynomials, Match., 28(1992), 139–150.
  • Haynes, T.W., Hedetniemi, S.T., Slater, P.J., Fundamentals of Domination in Graphs, Marcel Dekker, New York, 1998.
  • Klavzar, S., Mollard, M., Wiener index and Hosoya polynomial of Fibonacci and Lucas qubes, MATCH Commun. Math. Comput. Chem., 68(2012), 311–324.
  • Majstorovic, S., Doslic, T., Klobucar, A., k-domination on hexagonal cactus chains, Kragujevac Journal of Mathematics, 2(2012), 335–347.
  • Vukicevic, D., Klobucar A., k-dominating sets on linear benzenoids and on the infinite hexagonal grid, Croatica Chemica Acta, 80(2)(2007), 187–191.
There are 8 citations in total.

Details

Primary Language English
Journal Section Articles
Authors

Bünyamin Şahin

Abdulgani Şahin

Publication Date December 28, 2018
Published in Issue Year 2018 Volume: 9

Cite

APA Şahin, B., & Şahin, A. (2018). On Domination Polynomials of Caterpillar Graphs. Turkish Journal of Mathematics and Computer Science, 9, 34-38.
AMA Şahin B, Şahin A. On Domination Polynomials of Caterpillar Graphs. TJMCS. December 2018;9:34-38.
Chicago Şahin, Bünyamin, and Abdulgani Şahin. “On Domination Polynomials of Caterpillar Graphs”. Turkish Journal of Mathematics and Computer Science 9, December (December 2018): 34-38.
EndNote Şahin B, Şahin A (December 1, 2018) On Domination Polynomials of Caterpillar Graphs. Turkish Journal of Mathematics and Computer Science 9 34–38.
IEEE B. Şahin and A. Şahin, “On Domination Polynomials of Caterpillar Graphs”, TJMCS, vol. 9, pp. 34–38, 2018.
ISNAD Şahin, Bünyamin - Şahin, Abdulgani. “On Domination Polynomials of Caterpillar Graphs”. Turkish Journal of Mathematics and Computer Science 9 (December 2018), 34-38.
JAMA Şahin B, Şahin A. On Domination Polynomials of Caterpillar Graphs. TJMCS. 2018;9:34–38.
MLA Şahin, Bünyamin and Abdulgani Şahin. “On Domination Polynomials of Caterpillar Graphs”. Turkish Journal of Mathematics and Computer Science, vol. 9, 2018, pp. 34-38.
Vancouver Şahin B, Şahin A. On Domination Polynomials of Caterpillar Graphs. TJMCS. 2018;9:34-8.