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Edge-Vertex Dominating Sets and Edge-Vertex Domination Polynomials of Cycles

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DOI: 10.4236/ojdm.2015.54007    3,103 Downloads   3,780 Views   Citations

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.

Conflicts of Interest

The authors declare no conflicts of interest.

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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