Issues‎ > ‎vol19n1‎ > ‎

Results on the Domination Polynomial of Some Coalescence Graphs

Nechirvan Badal Ibrahim1, Haven Jalal Ahmed1

1 Department of Mathematics, College of Science, University of Duhok, 
Kurdistan Region, Iraq.

Original: 25 January 2016, Revised: 26 Octobre 2016, Accepted: 20 November 2016, Published online: 20 March 2017



In this paper, we obtain the domination polynomial of some coalescence of a complete Kn and wheel Wn graphs such as edge introducing, vertex identification, coneighboracation graph, edge identified graph, t-tuple coalescence graphs and b-bridge tuple coalescence graphs with some special graphs.

Key Words:
T-tuple coalescence,
B-bridge coalescence, 
Domination polynomial.


[1] Alikhani, S. "On the Domination Polynomial of Some Graph Operations” ISRN Combin., Vol. 2013, Article ID 146595, 3 pages. (2013). 

[2] Alikhani, S. and Peng, Y-h."Dominating sets and domination polynomials of certain graphs, II" Opuscula Mathematica , Vol. 30, No. 1, pp. 37–51. (2010).

[3] Alikhani, S. and Peng, Y-h. "Introduction to Domination Polynomial of a Graph". Ars Combin.,    Vol. 114, pp. 257-266. (2014).

[4] Balakrishnan, R. and Ranganathan, K. "A Textbook of Graph Theory" Springer, New York. (2012).

[5] Ibrahim, N.B. "On the Nullity of Some Sequential Element Identified, Element Introduced Graphs". M.Sc. . Thesis, University of Zakho, Iraq, (2013).

[6] Kahat, S. Sh, Khalaf, A. J. and Hasni, R. "Dominating Sets and Domination Polynomials of Stars" Australian Journal of Basic and Applied Sciences, Vol. 8, No. 6, pp. 383-386. (2014).

[7] Kahat, S. Sh., Khalaf, A. J. and Hasni, R. "Dominating Sets and Domination Polynomial of Wheels" Asian Journal of Applied Sciences, Vol. 02, No.  03, pp. 287-290, (2014).

[8] Kotek, T., Preen, J., Frank, S., Peter, T. and Martin, T. "Recurrence relations and splitting formulas for the domination polynomial". The Electronic Journal of Combinatorics, Vol. 19, No. 3, pp. 1- 27, (2012).

[9] Kotek, T. and Preen, J. "Domination Polynomials of Graph Products" arXiv:1305.1475v2, math.CO., (2013).