{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,14]],"date-time":"2025-10-14T11:33:30Z","timestamp":1760441610608,"version":"3.41.2"},"reference-count":0,"publisher":"The Electronic Journal of Combinatorics","issue":"1","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Electron. J. Combin."],"abstract":"<jats:p>The queen's graph $Q_{n}$ has the squares of the $n \\times n$ chessboard as its vertices; two squares are adjacent if they are in the same row, column, or diagonal. Let $\\gamma (Q_{n})$ and $i(Q_{n})$ be the minimum sizes of a dominating set and an independent dominating set of $Q_{n}$, respectively. Recent results, the Parallelogram Law, and a search algorithm adapted from Knuth are used to find dominating sets. New values and bounds:(A) $\\gamma (Q_n) = \\lceil n\/2 \\rceil$ is shown for 17 values of $n$ (in particular, the set of values for which the conjecture $\\gamma (Q_{4k+1}) = 2k + 1$ is known to hold is extended to $k \\leq 32$);(B) $i(Q_n) = \\lceil n\/2 \\rceil$ is shown for 11 values of $n$, including 5 of those from (A);(C) One or both of $\\gamma (Q_n)$ and $i(Q_n)$ is shown to lie in $\\{ \\lceil n\/2 \\rceil $, $\\lceil n\/2 \\rceil + 1 \\}$ for 85 values of $n$ distinct from those in (A) and (B).Combined with previously published work, these results imply that for $n \\leq 120$, each of $\\gamma (Q_n)$ and $i(Q_n)$ is either known, or known to have one of two values.Also, the general bounds $\\gamma (Q_n) \\leq 69n\/133 + O(1)$ and $i(Q_n) \\leq 61n\/111 + O(1)$ are established.\u00a0Comment added August 25th 2003.Corrigendum added October 5th 2017.\u00a0<\/jats:p>","DOI":"10.37236\/1573","type":"journal-article","created":{"date-parts":[[2020,1,11]],"date-time":"2020-01-11T02:08:55Z","timestamp":1578708535000},"source":"Crossref","is-referenced-by-count":11,"title":["Values of Domination Numbers of the Queen's Graph"],"prefix":"10.37236","volume":"8","author":[{"given":"Patric R. J.","family":"\u00d6sterg\u00e5rd","sequence":"first","affiliation":[]},{"given":"William D.","family":"Weakley","sequence":"additional","affiliation":[]}],"member":"23455","published-online":{"date-parts":[[2001,3,26]]},"container-title":["The Electronic Journal of Combinatorics"],"original-title":[],"link":[{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v8i1r29\/pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v8i1r29\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2020,1,18]],"date-time":"2020-01-18T05:18:17Z","timestamp":1579324697000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/view\/v8i1r29"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2001,3,26]]},"references-count":0,"journal-issue":{"issue":"1","published-online":{"date-parts":[[2001,1,1]]}},"URL":"https:\/\/doi.org\/10.37236\/1573","relation":{},"ISSN":["1077-8926"],"issn-type":[{"type":"electronic","value":"1077-8926"}],"subject":[],"published":{"date-parts":[[2001,3,26]]},"article-number":"R29"}}