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arXiv · 0905.3268

Dominating sets and Domination polynomials of Cycles

Saeid Alikhani·Yee-hock Peng
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Abstract

Let G=(V,E) be a simple graph. A set S\subset V is a dominating set of G, if every vertex in V§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.

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Saeid Alikhani, Yee-hock Peng. 2009-05-20. Dominating sets and Domination polynomials of Cycles. https://arxiv.org/abs/0905.3268

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