Domination Polynomial of the Rook Graph
Stephan Mertens
Institut für Physik
Otto-von-Guericke Universität Magdeburg
Postfach 4120
39016 Magdeburg
Germany
and
Santa Fe Institute
1399 Hyde Park Rd
Santa Fe, NM 87501
USA
Abstract:
A placement of chess pieces on a chessboard is called dominating if each
free square of the chessboard is under attack by at least one piece. In
this contribution we compute the number of dominating arrangements of k
rooks on an n × m chessboard.
To this end we derive an expression for
the corresponding generating function, the domination polynomial of the
n × m rook graph.
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(Concerned with sequences
A006075
A055599
A075458
A287274
A368831.)
Received December 31 2023; revised version received March 5 2024.
Published in Journal of Integer Sequences,
March 9 2024.
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