Dominating Sets and Domination Polynomials of Cycles
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 Ci n be the family of dominating sets of a cycle Cn with cardinality i, and let d(Cn, i) = |Ci n|. In this paper, we construct Ci n,and obtain a recursive formu...
| Main Authors: | , |
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| Format: | Article |
| Language: | English English |
| Published: |
2008
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| Online Access: | http://psasir.upm.edu.my/id/eprint/7111/ http://psasir.upm.edu.my/id/eprint/7111/1/136.pdf |
| Summary: | 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 Ci n be the family of dominating sets of a cycle Cn with cardinality i, and let d(Cn, i) = |Ci n|. In this paper, we construct Ci n,and obtain a recursive formula for d(Cn, i). Using this recursive formula, we consider the polynomial D(Cn, x) = Pn
i=⌈ n 3 ⌉ d(Cn, i)xi, which we call domination polynomial of cycles and obtain some properties of this polynomial. |
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