Dominating Sets and Domination Polynomials of Cycles
نویسنده
چکیده
Let G = (V,E) be a simple graph. A set S ⊆ V is a dominating set of G, if every vertex in V \S is adjacent to at least one vertex in S. Let C n be the family of dominating sets of a cycle Cn with cardinality i, and let d(Cn, i) = |C i n|. In this paper, we construct C i n, and obtain a recursive formula for d(Cn, i). Using this recursive formula, we consider the polynomial D(Cn, x) = ∑n i=⌈n 3 ⌉ d(Cn, i)x , which we call domination polynomial of cycles and obtain some properties of this polynomial.
منابع مشابه
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تاریخ انتشار 2009