Dominating Sets and Domination Polynomials of Paths

Saeid Alikhani and Yee-Hock Peng

International Journal of Mathematics and Mathematical Sciences, 2009, vol. 2009, 1-10

Abstract:

Let be a simple graph. A set is a dominating set of , if every vertex in is adjacent to at least one vertex in . Let be the family of all dominating sets of a path with cardinality , and let . In this paper, we construct , and obtain a recursive formula for . Using this recursive formula, we consider the polynomial , which we call domination polynomial of paths and obtain some properties of this polynomial.

Date: 2009
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jijmms:542040

DOI: 10.1155/2009/542040

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