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 OJDM  Vol.5 No.4 , October 2015
Edge-Vertex Dominating Sets and Edge-Vertex Domination Polynomials of Cycles
Abstract: Let G = (V, E) be a simple graph. A set S E(G) is an edge-vertex dominating set of G (or simply an ev-dominating set), if for all vertices v V(G); there exists an edge eS such that e dominates v. Let denote the family of all ev-dominating sets of with cardinality i. Let . In this paper, we obtain a recursive formula for . Using this recursive formula, we construct the polynomial, , which we call edge-vertex domination polynomial of (or simply an ev-domination polynomial of ) and obtain some properties of this polynomial.
Cite this paper: Vijayan, A. and Sherin Beula, J. (2015) Edge-Vertex Dominating Sets and Edge-Vertex Domination Polynomials of Cycles. Open Journal of Discrete Mathematics, 5, 74-87. doi: 10.4236/ojdm.2015.54007.
References

[1]   Sampath Kumar, E. and Kamath, S.S. (1992) Mixed Domination in Graphs. Sankhya: The Indian Journal of Statistics, 54, 399-402.

[2]   Alikhani, S. and Peng, Y.-H. (2009) Dominating Sets and Domination Polynomials of Paths. International Journal of Mathematics and Mathematical Sciences, 2009, Article ID: 542040.
http://dx.doi.org/10.1155/2009/542040

[3]   Alikhani, S. and Peng, Y.-H. (2009) Dominating Sets and Domination Polynomials of Cycles.

[4]   Vijayan, A. and Sherin Beula, J. (2014) ev-Dominating Sets and ev-Domination Polynomials of Paths. International Organization of Scientific Research Journal of Mathematics, 10, 7-17.

[5]   Vijayan, A. and Lal Gipson, K. (2013) Dominating Sets and Domination Polynomials of Square of Paths. Open Journal of Discrete Mathematics, 3, 60-69.

[6]   Chartand, G. and Zhang, P. (2005) Introduction to Graph Theory. McGraw-Hill, Boston.

[7]   Alikhani, S. and Peng, Y.-H. (2009) Introduction to Domination Polynomial of a Graph.

 
 
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