Matches in SemOpenAlex for { <https://semopenalex.org/work/W2415629108> ?p ?o ?g. }
Showing items 1 to 77 of
77
with 100 items per page.
- W2415629108 abstract "The queen's graph $Q_{m times n}$ has the squares of the $m times n$ chessboard as its vertices; two squares are adjacent if they are in the same row, column, or diagonal of the board. A set $D$ of squares of $Q_{m times n}$ is a dominating set for $Q_{m times n}$ if every square of $Q_{m times n}$ is either in $D$ or adjacent to a square in $D$. The minimum size of a dominating set of $Q_{m times n}$ is the domination number, denoted by $gamma(Q_{m times n})$. Values of $gamma(Q_{m times n}), , 4 leq m leq n leq 18, ,$ are given here, in each case with a file of minimum dominating sets (often all of them, up to symmetry) in an online appendix at this https URL. In these ranges for $m$ and $n$, monotonicity fails once: $gamma(Q_{8 times 11}) = 6 > 5 = gamma(Q_{9 times 11}) = gamma(Q_{10 times 11}) = gamma(Q_{11 times 11})$. Lower bounds on $gamma(Q_{m times n})$ are given. In particular, if $m leq n$ then $gamma(Q_{m times n}) geq min { m, lceil (m+n-2)/4 rceil }$. A set of squares is independent if no two of its squares are adjacent. The minimum size of an independent dominating set of $Q_{m times n}$ is the independent domination number, denoted by $i(Q_{m times n})$. Values of $i(Q_{m times n}), , 4 leq m leq n leq 18, ,$ are given here, in each case with some minimum dominating sets. In these ranges for $m$ and $n$, monotonicity fails twice: $i(Q_{8 times 11}) = 6 > 5 = i(Q_{9 times 11}) = i(Q_{10 times 11}) = i(Q_{11 times 11})$, and $i(Q_{11 times 18}) = 9 > 8 = i(Q_{12 times 18})$." @default.
- W2415629108 created "2016-06-24" @default.
- W2415629108 creator A5019174790 @default.
- W2415629108 creator A5031500684 @default.
- W2415629108 creator A5042358724 @default.
- W2415629108 creator A5068316228 @default.
- W2415629108 date "2016-06-07" @default.
- W2415629108 modified "2023-09-27" @default.
- W2415629108 title "Domination of the rectangular queen's graph" @default.
- W2415629108 cites W1487888965 @default.
- W2415629108 cites W1511873780 @default.
- W2415629108 cites W17350985 @default.
- W2415629108 cites W1884457451 @default.
- W2415629108 cites W1964459245 @default.
- W2415629108 cites W2001655229 @default.
- W2415629108 cites W2014767907 @default.
- W2415629108 cites W2019635364 @default.
- W2415629108 cites W2072177531 @default.
- W2415629108 cites W2072808306 @default.
- W2415629108 cites W2110753888 @default.
- W2415629108 cites W2188337130 @default.
- W2415629108 cites W2752613978 @default.
- W2415629108 cites W2762915491 @default.
- W2415629108 cites W2988320476 @default.
- W2415629108 cites W3038027991 @default.
- W2415629108 hasPublicationYear "2016" @default.
- W2415629108 type Work @default.
- W2415629108 sameAs 2415629108 @default.
- W2415629108 citedByCount "0" @default.
- W2415629108 crossrefType "posted-content" @default.
- W2415629108 hasAuthorship W2415629108A5019174790 @default.
- W2415629108 hasAuthorship W2415629108A5031500684 @default.
- W2415629108 hasAuthorship W2415629108A5042358724 @default.
- W2415629108 hasAuthorship W2415629108A5068316228 @default.
- W2415629108 hasConcept C114614502 @default.
- W2415629108 hasConcept C130367717 @default.
- W2415629108 hasConcept C132525143 @default.
- W2415629108 hasConcept C135692309 @default.
- W2415629108 hasConcept C146661039 @default.
- W2415629108 hasConcept C2524010 @default.
- W2415629108 hasConcept C33923547 @default.
- W2415629108 hasConcept C80899671 @default.
- W2415629108 hasConceptScore W2415629108C114614502 @default.
- W2415629108 hasConceptScore W2415629108C130367717 @default.
- W2415629108 hasConceptScore W2415629108C132525143 @default.
- W2415629108 hasConceptScore W2415629108C135692309 @default.
- W2415629108 hasConceptScore W2415629108C146661039 @default.
- W2415629108 hasConceptScore W2415629108C2524010 @default.
- W2415629108 hasConceptScore W2415629108C33923547 @default.
- W2415629108 hasConceptScore W2415629108C80899671 @default.
- W2415629108 hasLocation W24156291081 @default.
- W2415629108 hasOpenAccess W2415629108 @default.
- W2415629108 hasPrimaryLocation W24156291081 @default.
- W2415629108 hasRelatedWork W109072738 @default.
- W2415629108 hasRelatedWork W1590248699 @default.
- W2415629108 hasRelatedWork W1968308625 @default.
- W2415629108 hasRelatedWork W1972652019 @default.
- W2415629108 hasRelatedWork W2057090129 @default.
- W2415629108 hasRelatedWork W2065461754 @default.
- W2415629108 hasRelatedWork W2089817321 @default.
- W2415629108 hasRelatedWork W2107079802 @default.
- W2415629108 hasRelatedWork W2766781494 @default.
- W2415629108 hasRelatedWork W2770835395 @default.
- W2415629108 hasRelatedWork W2797561846 @default.
- W2415629108 hasRelatedWork W2951821892 @default.
- W2415629108 hasRelatedWork W2953009631 @default.
- W2415629108 hasRelatedWork W2979119835 @default.
- W2415629108 hasRelatedWork W2999204739 @default.
- W2415629108 hasRelatedWork W3024996095 @default.
- W2415629108 hasRelatedWork W3082126129 @default.
- W2415629108 hasRelatedWork W3084403602 @default.
- W2415629108 hasRelatedWork W3102706553 @default.
- W2415629108 hasRelatedWork W65264223 @default.
- W2415629108 isParatext "false" @default.
- W2415629108 isRetracted "false" @default.
- W2415629108 magId "2415629108" @default.
- W2415629108 workType "article" @default.