Upper bounds for the domination numbers of toroidal queens graphs

Christina M. Mynhardt

Discussiones Mathematicae Graph Theory (2003)

  • Volume: 23, Issue: 1, page 163-175
  • ISSN: 2083-5892

Abstract

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We determine upper bounds for γ ( Q n t ) and i ( Q ₙ t ) , the domination and independent domination numbers, respectively, of the graph Q ₙ t obtained from the moves of queens on the n×n chessboard drawn on the torus.

How to cite

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Christina M. Mynhardt. "Upper bounds for the domination numbers of toroidal queens graphs." Discussiones Mathematicae Graph Theory 23.1 (2003): 163-175. <http://eudml.org/doc/270444>.

@article{ChristinaM2003,
abstract = {We determine upper bounds for $γ(Qn^t)$ and $i(Qₙ^t)$, the domination and independent domination numbers, respectively, of the graph $Qₙ^t$ obtained from the moves of queens on the n×n chessboard drawn on the torus.},
author = {Christina M. Mynhardt},
journal = {Discussiones Mathematicae Graph Theory},
keywords = {queens graph; toroidal chessboards; queens domination problem; independent domination number; toroidal chessboard},
language = {eng},
number = {1},
pages = {163-175},
title = {Upper bounds for the domination numbers of toroidal queens graphs},
url = {http://eudml.org/doc/270444},
volume = {23},
year = {2003},
}

TY - JOUR
AU - Christina M. Mynhardt
TI - Upper bounds for the domination numbers of toroidal queens graphs
JO - Discussiones Mathematicae Graph Theory
PY - 2003
VL - 23
IS - 1
SP - 163
EP - 175
AB - We determine upper bounds for $γ(Qn^t)$ and $i(Qₙ^t)$, the domination and independent domination numbers, respectively, of the graph $Qₙ^t$ obtained from the moves of queens on the n×n chessboard drawn on the torus.
LA - eng
KW - queens graph; toroidal chessboards; queens domination problem; independent domination number; toroidal chessboard
UR - http://eudml.org/doc/270444
ER -

References

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  1. [1] W. Ahrens, Mathematische Unterhalten und Spiele (B.G. Teubner, Leipzig-Berlin, 1910). 
  2. [2] M. Bezzel, Schachfreund, Berliner Schachzeitung, 3 (1848) 363. 
  3. [3] A.P. Burger, E.J. Cockayne and C.M. Mynhardt, Queens graphs for chessboards on the torus, Australas. J. Combin. 24 (2001) 231-246. Zbl0979.05080
  4. [4] A.P. Burger and C.M. Mynhardt, Symmetry and domination in queens graphs, Bulletin of the ICA 29 (2000) 11-24. Zbl0954.05034
  5. [5] A.P. Burger and C.M. Mynhardt, Properties of dominating sets of the queens graph Q 4 k + 3 , Utilitas Math. 57 (2000) 237-253. Zbl0955.05076
  6. [6] A.P. Burger and C.M. Mynhardt, An improved upper bound for queens domination numbers, Discrete Math., to appear. Zbl1015.05066
  7. [7] A.P. Burger, C.M. Mynhardt and W.D. Weakley, The domination number of the toroidal queens graph of size 3k × 3k, Australas. J. Combin., to appear. Zbl1030.05094
  8. [8] E.J. Cockayne, Chessboard Domination Problems, Discrete Math. 86 (1990) 13-20, doi: 10.2307/2325220. Zbl0818.05057
  9. [13] P.R.J. Östergå rd and W.D. Weakley, Values of domination numbers of the queen's graph, Electron. J. Combin. 8 (2001) no. 1, Research paper 29, 19 pp. 
  10. [14] W.D. Weakley, Domination In The Queen's Graph, in: Y. Alavi and A.J. Schwenk, eds, Graph Theory, Combinatorics, and Algorithms, Volume 2, pages 1223-1232 (Wiley-Interscience, New York, 1995). Zbl0842.05053
  11. [15] W.D. Weakley, A lower bound for domination numbers of the queen's graph, J. Combin. Math. Combin. Comput., to appear. Zbl1012.05124
  12. [16] W.D. Weakley, Upper bounds for domination numbers of the queen's graph, Discrete Math. 242 (2002) 229-243, doi:10.1016/S0012-365X(00)00467-2. 

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