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

Affiliation(s)

^{1}
Department of Mathematics, Nesamony Memorial Christian College, Marthandam, India.

^{2}
Department of Mathematics, Mar Ephraem College of Engineering & Technology, Marthandam, India.

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 *e**S* 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.

Let

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.

Vijayan, A. and Sherin Beula, J. (2015) Edge-Vertex Dominating Sets and Edge-Vertex Domination Polynomials of Cycles.

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.

[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.