Abstract | ||
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The queen's graph Q(n) has the squares of the n x n chessboard as its vertices; two squares are adjacent if they are in the same row, column, or diagonal. Let gamma(Q(n)) be the minimum size of a dominating set of Q(n) It has been proved that gamma(Q(n)) >= (n - 1)/2 for all n. Known dominating sets imply that gamma(Q(n)) = (n - 1)/2 for n = 3,11. We show that gamma(Q(n)) = (n - 1)/2 only for n = 3,11, and thus that gamma(Q(n)) >= inverted right perpendicular n/2 inverted left perpendicular for all other positive integers n. |
Year | Venue | Field |
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2007 | AUSTRALASIAN JOURNAL OF COMBINATORICS | Graph,Combinatorics,Upper and lower bounds,Mathematics |
DocType | Volume | ISSN |
Journal | 37 | 2202-3518 |
Citations | PageRank | References |
2 | 0.38 | 0 |
Authors | ||
2 |
Name | Order | Citations | PageRank |
---|---|---|---|
dmitry finozhenok | 1 | 2 | 0.38 |
William D. Weakley | 2 | 56 | 10.40 |