|
%I #25 Sep 03 2021 09:37:56
%S 1,1,2,2,3,3,3,4,4,5,5,6,6,7,7,8,8,9,9,9,10,10,11,11
%N Domination number for rook graph HR(n) on a triangular board of hexagonal cells. The rook can move along any row of adjacent cells, in any of the three directions.
%C The value for HR(20) was obtained by Rob Pratt, Sep 29 2013, using integer-linear programming.
%D J. Konhauser, D. Velleman, S. Wagon, Which Way Did the Bicycle Go? Washington, DC, Math. Assoc. of America, 1996, pp. 169-172
%H William Herbert Bird, <a href="https://dspace.library.uvic.ca/handle/1828/8634">Computational methods for domination problems</a>, University of Victoria, 2017. See Table 2.4 on p. 32.
%H J. DeMaio and H. L. Tran, <a href="http://www.jstor.org/stable/10.4169/college.math.j.44.4.307">Domination and independence on a triangular honeycomb chessboard</a>, Coll. Math. J. 44 (2013) 307-314.
%H Stan Wagon, <a href="http://www.jstor.org/stable/10.4169/college.math.j.45.4.278">Graph Theory Problems from Hexagonal and Traditional Chess</a>, The College Mathematics Journal, Vol. 45, No. 4, September 2014, pp. 278-287
%e For HR(7), the graph can be dominated by the three vertices 6, 11, 26, where we count down from the top.
%e This graph was called the Queen graph in the DeMaio and Tran paper, but the moves are those of a rook in the classic hexagonal chess game.
%Y Cf. A075458, A075324, A075561, A006075.
%K nonn,hard,more
%O 1,3
%A _Stan Wagon_, Sep 29 2013
%E a(21)-a(24) from Bird added by _Andrey Zabolotskiy_, Sep 03 2021
|
