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

A. Vijayan; J. Sherin Beula

doi:10.4236/ojdm.2015.54007

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Open Journal of Discrete Mathematics > Vol.5 No.4, October 2015

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

A. Vijayan¹, J. Sherin Beula^2*

¹Department of Mathematics, Nesamony Memorial Christian College, Marthandam, India.
²Department of Mathematics, Mar Ephraem College of Engineering & Technology, Marthandam, India.

DOI: 10.4236/ojdm.2015.54007 PDF HTML XML 3,214 Downloads 3,987 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.

Keywords

ev-Domination Set, ev-Domination Number, ev-Domination Polynomials

Share and Cite:

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.

Conflicts of Interest

The authors declare no conflicts of interest.

References

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[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.