Dominating sets and Domination polynomials of Cycles

Details Dominating sets and Domination polynomials of Cycles Dominating sets and Domination polynomials of Cycles

2009-05-20

arxiv.org/abs/0905.3268v1

Mathematics

Combinatorics

13 pages. Accepted in http://www.ripublication.com/gjpam.htm

Scientific paper

Let G=(V,E) be a simple graph. A set S\subset V is a dominating set of G, if every vertex in V\S is adjacent to at least one vertex in S. Let {\mathcal C}_n^i be the family of dominating sets of a cycle C_n with cardinality i, and let d(C_n,i) = |{\mathcal C}_n^i. In this paper, we construct {\mathcal C}_n^i, and obtain a recursive formula for d(C_n, i). Using this recursive formula, we consider the polynomial D(C_n, x) = \sum_{i=1}^n d(C_n, i)x^i, which we call domination polynomial of cycles and obtain some properties of this polynomial.

Affiliated with

Also associated with

No associations

Rating

Dominating sets and Domination polynomials of Cycles does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Dominating sets and Domination polynomials of Cycles, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Dominating sets and Domination polynomials of Cycles will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-242669