On Domination Polynomials of Caterpillar Graphs

Yıl 2018, Cilt: 9, 34 - 38, 28.12.2018

Bünyamin Şahin Abdulgani Şahin

Öz

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.

Anahtar Kelimeler

Domination Polynomial, Caterpillar graph

Kaynakça

• 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.