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math.CO2024
Domination Polynomials of the Grid, the Cylinder, the Torus, and the King Graph
Stephan Mertens
We present an algorithm to compute the domination polynomial of the grid, cylinder, and torus graphs and the king graph. The time complexity of the algorithm is $O(m^2…
math.CO2024
Domination by kings is oddly even
Cristopher Moore, Stephan Mertens
The king graph consists of all locations on an chessboard, where edges are legal moves of a chess king. %where each vertex represents a square on a chessb…
math.CO2024
Domination Polynomial of the Rook Graph
Stephan Mertens
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 n…