On Domination Polynomials of Caterpillar Graphs
Year 2018,
Volume: 9, 34 - 38, 28.12.2018
Bünyamin Şahin
,
Abdulgani Şahin
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
Bünyamin Şahin
,
Abdulgani Şahin
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.