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For a positive integer n, considering the \(n\times n\) chessboard, for a chess piece P, one is interested in the graph \(P_{n}\) by taking the squares of the chessboard as its vertices where two squares are adjacent if the piece P situated at one of the squares is able to move directly to the other. After recalling some known results and open questions on the domination number \(\gamma (P_n)\) for the square board \(P_n\) , we here introduce some new questions.

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Chessboard Domination: Introduction of Some New Problems

  • 会议论文

  • 发表日期：

    2025年

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  • S. D. Adhikari,
  • Shruti Hegde,
  • Md Ibrahim Molla

摘要

For a positive integer n, considering the \(n\times n\) chessboard, for a chess piece P, one is interested in the graph \(P_{n}\) by taking the squares of the chessboard as its vertices where two squares are adjacent if the piece P situated at one of the squares is able to move directly to the other. After recalling some known results and open questions on the domination number \(\gamma (P_n)\) for the square board \(P_n\) , we here introduce some new questions.