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Independence and domination on shogiboard graphs
| Content Provider | Scilit |
|---|---|
| Author | Chatham, Doug |
| Copyright Year | 2017 |
| Abstract | Given a (symmetrically-moving) piece from a chesslike game, such as shogi, and an n×n board, we can form a graph with a vertex for each square and an edge between two vertices if the piece can move from one vertex to the other. We consider two pieces from shogi: the dragon king, which moves like a rook and king from chess, and the dragon horse, which moves like a bishop and rook from chess. We show that the independence number for the dragon kings graph equals the independence number for the queens graph. We show that the (independent) domination number of the dragon kings graph is n − 2 for 4 ≤ n ≤ 6 and n − 3 for n ≥ 7. For the dragon horses graph, we show that the independence number is 2n − 3 for n ≥ 5, the domination number is at most n−1 for n ≥ 4, and the independent domination number is at most n for n ≥ 5. |
| Related Links | https://content.sciendo.com/downloadpdf/journals/rmm/4/8/article-p25.pdf http://www.degruyter.com/downloadpdf/j/rmm.2017.4.issue-8/rmm-2017-0018/rmm-2017-0018.xml |
| Ending Page | 37 |
| Page Count | 13 |
| Starting Page | 25 |
| e-ISSN | 21821976 |
| DOI | 10.1515/rmm-2017-0018 |
| Journal | Recreational Mathematics Magazine |
| Issue Number | 8 |
| Volume Number | 4 |
| Language | English |
| Publisher | Walter de Gruyter GmbH |
| Publisher Date | 2017-12-20 |
| Access Restriction | Open |
| Subject Keyword | Recreational Mathematics Magazine Applied Mathematics Shogi N-queens Problem Combinatorics Journal: Recreational Mathematics Magazine, Vol- 4 |
| Content Type | Text |
| Resource Type | Article |
