Domination polynomials of  cubic graphs of order 10

Saeid ALIKHANI

Article Details

Domination polynomials of cubic graphs of order 10

Authors:

Saeid ALIKHANI

Publisher:

TUBITAK

Journal:

Turkish Journal of Mathematics 2011 Vol.35 Issue 3, pp.355-366

Document Type:

Article

Publication Date:

2/2011

Document Language:

Turkish

Document ID (Org No.):

2000747923

Frequency:

Bimonthly

eISSN:

1303-6149

pISSN:

1300-0098

Keywords:

Abstract:

 

Let G be a simple graph of order n.  The domination  polynomial of G is the polynomial D(G,x)=\sumi=g(G)n d(G,i)  xi, where d(G,i) is the number of dominating sets of G of size i, and  g(G) is the domination number of G. In this paper we study the  domination polynomials of cubic graphs of order 10.  As a consequence,  we show that the Petersen graph is determined uniquely by its  domination polynomial.

 

Let G be a simple graph of order n.  The domination  polynomial of G is the polynomial D(G,x)=\sumi=g(G)n d(G,i)  xi, where d(G,i) is the number of dominating sets of G of size i, and  g(G) is the domination number of G. In this paper we study the  domination polynomials of cubic graphs of order 10.  As a consequence,  we show that the Petersen graph is determined uniquely by its  domination polynomial.

Article Details

Domination polynomials of cubic graphs of order 10

Authors:

Saeid ALIKHANI

Publisher:

TUBITAK

Journal:

Turkish Journal of Mathematics 2011 Vol.35 Issue 3, pp.355-366

Document Type:

Article

Publication Date:

2/2011

Document Language:

Turkish

Document ID (Org No.):

2000747923

Frequency:

Bimonthly

eISSN:

1303-6149

pISSN:

1300-0098

Domination polynomial

equivalence class

petersen graph

cubic graphs

Issues

Article Details

Domination polynomials of cubic graphs of order 10

Authors: Saeid ALIKHANI

Publisher: TUBITAK

Journal: Turkish Journal of Mathematics 2011 Vol.35 Issue 3, pp.355-366

Document Type: Article

Publication Date: 2/2011

Document Language: Turkish

Document ID (Org No.): 2000747923

Frequency: Bimonthly

eISSN: 1303-6149

pISSN: 1300-0098

Domination polynomial

equivalence class

petersen graph

cubic graphs

Issues

Authors:

Saeid ALIKHANI

Publisher:

TUBITAK

Journal:

Turkish Journal of Mathematics 2011 Vol.35 Issue 3, pp.355-366

Document Type:

Article

Publication Date:

2/2011

Document Language:

Turkish

Document ID (Org No.):

2000747923

Frequency:

Bimonthly

eISSN:

1303-6149

pISSN:

1300-0098