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 |
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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 |
| _version_ | 1848840504926535680 |
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| author | Alikhania, Saeid Yee-hock, Peng |
| author_facet | Alikhania, Saeid Yee-hock, Peng |
| author_sort | Alikhania, Saeid |
| building | UPM Institutional Repository |
| collection | Online Access |
| description | 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. |
| first_indexed | 2025-11-15T07:28:24Z |
| format | Article |
| id | upm-7111 |
| institution | Universiti Putra Malaysia |
| institution_category | Local University |
| language | English English |
| last_indexed | 2025-11-15T07:28:24Z |
| publishDate | 2008 |
| recordtype | eprints |
| repository_type | Digital Repository |
| spelling | upm-71112013-05-27T07:33:27Z http://psasir.upm.edu.my/id/eprint/7111/ Dominating Sets and Domination Polynomials of Cycles Alikhania, Saeid Yee-hock, Peng 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. 2008 Article PeerReviewed application/pdf en http://psasir.upm.edu.my/id/eprint/7111/1/136.pdf Alikhania, Saeid and Yee-hock, Peng (2008) Dominating Sets and Domination Polynomials of Cycles. Global Journal of Pure And Applied Mathematics, 4 (2). pp. 202-210. http://arxiv.org/PS_cache/arxiv/pdf/0905/0905.3268v1.pdf English |
| spellingShingle | Alikhania, Saeid Yee-hock, Peng Dominating Sets and Domination Polynomials of Cycles |
| title | Dominating Sets and Domination Polynomials of Cycles |
| title_full | Dominating Sets and Domination Polynomials of Cycles |
| title_fullStr | Dominating Sets and Domination Polynomials of Cycles |
| title_full_unstemmed | Dominating Sets and Domination Polynomials of Cycles |
| title_short | Dominating Sets and Domination Polynomials of Cycles |
| title_sort | dominating sets and domination polynomials of cycles |
| url | http://psasir.upm.edu.my/id/eprint/7111/ http://psasir.upm.edu.my/id/eprint/7111/ http://psasir.upm.edu.my/id/eprint/7111/1/136.pdf |