Paired, Total, and Connected Domination on the Queen's Graph Revisited

Paul A. Burchett
2016 Open Journal of Discrete Mathematics  
The question associated with total domination on the queen's graph has a long and rich history, first having been posed by Ahrens in 1910 [1]. The question is this: What is the minimum number of queens needed so that every square of an n × n board is attacked? Beginning in 2005 with Amirabadi, Burchett, and Hedetniemi [2] [3], work on this problem, and two other related problems, has seen progress. Bounds have been given for the values of all three domination parameters on the queen's graph. In
more » ... e queen's graph. In this paper, formations of queens are given that provide new bounds for the values of total, paired, and connected domination on the queen's graph, denoted ( ) n ≡ 4 mod6 .
doi:10.4236/ojdm.2016.61001 fatcat:3oe76nduh5abfd3ybnc24rwmoi