International Journal of Mathematical Sciences and Computing(IJMSC)
ISSN: 2310-9025 (Print), ISSN: 2310-9033 (Online)
Published By: MECS Press
IJMSC Vol.6, No.6, Dec. 2020
Vertex Connected Domination Polynomial of some Coalescence of Complete and Wheel Graphs
Full Text (PDF, 920KB), PP.1-8
In this paper, we introduce new results of vertex connected dominating set and vertex connected domination polynomial of vertex identification, edge introduced and t-tuple of complete graph, also we determine new results of vertex connected dominating set and vertex connected domination polynomial of vertex identification, edge introduced and t-tuple of wheel graph.
Cite This Paper
Nechirvan Badal Ibrahim, Hariwan Fadhil M.Salih. " Vertex Connected Domination Polynomial of some Coalescence of Complete and Wheel Graphs ", International Journal of Mathematical Sciences and Computing (IJMSC), Vol.6, No.6, pp.1-8, 2020. DOI: 10.5815/IJMSC.2020.06.01
 A. Vijayan, T.B. Anitha, G. Edwin, Connected Total Dominating Sets and Connected Total Domination Polynomials of Stars and Wheels, IOSR Journal of Mathematics, Vol. 11, No. 1, pp. 112-121, 2015.
 B. Askari and M. Alaeiyan, The vertex domination polynomial and edge domination polynomial of a graph, Acta Universitatis Apulensis , Vol. 28, pp. 157-162, 2011.
 B. Chaluvaraju , Puttaswamy, N. Manjunath and S. R. Nayaka, The co-connected Domination Polynomial of a Graph, Advances and Applications in Discrete Mathematics, Vol. 18, No. 1, pp.57-70, 2017.
 C. E. Go and S. R. Canoy, Jr., Domination in the corona and join of graphs, Int. Math. Forum, Vol. 6, No.16, pp. 763-771, 2011.
 E. Sampathkumar, H. B. Walikar, The Connected Domination Number of a Graph, J. Math. Phys. Sci., Vol.13, No. 6, pp. 607-613, 1979.
 F. Harary, Graph theory, Addison-Wesley, Reading Mass, 1969.
 J. Brown and J. Tufts, On the roots of domination polynomials, Graphs and Combinatorics, 2013.
 K. R. Sharaf, D. A. Ali, Nullity of t-Tupple Graphs, International Journal of Mathematical, Computational, Statistical, Natural and Physical Engineering Vol. 8, No. 2, pp. 314–324, 2014.
 M. B. V. Dhananjaya, G. Deepak, N. D. Soner, Connected Domination Polynomial of a Graph, International Journal of Mathematical Archive- Vol. 4 No. 11, pp. 90-96, 2013.
 N. B. Ibrahim1 and H. J. Ahmed, Results on the Domination Polynomial of Some Coalescence Graphs, Journal of Zankoy Sulaimani, Vol. 19, No. 1, pp.171-176, 2017.
 S. Alikhani and Y.-H. Peng, Dominating sets and domination polynomials of certain graphs. II, Opuscula Mathematica, Vol. 30, No. 1, pp. 37–51, 2010.
 S. Alikhani, Dominating sets and domination polynomials of graphs, Ph.D. thesis, Universiti Putra Malaysia, 2009.
 S. Alikhani, Y-h. Peng, Introduction to Domination Polynomial of a Graph, arXiv: 0905.2251v1, math.CO, 2009.
 T. Kotek, J. Preen, Recurrence relations and splitting formulas for the domination polynomial, The .Electronic Journal of Combinatorics, Vol. 19, No. 3, pp. 1-27, 2012.
 T. W. Haynes, S. T. Hedetniemi and P. J. Slater, Fundamentals of Domination in Graphs, Marcel Dekker, Inc., New York, 1998.