Relations Between SomePieces in The Game of Chess and Some Properties of Graphs

In this paper, the necessary conditions for a bipartite graph to be Hamiltonian are first discussed. Relating these conditions, the movements of a chess piece called Knight, in the game of chess are discussed. And it is shown that finding a Hamiltonian cycle in a given bipartite graph of 64 vertices is equivalent to finding a reentrant Knight’s tour on a8 x 8 chessboard. Furthermore, the domination concepts of graphs are discussed. Relating these conditions, the movements of a chess piece called Queen are discussed. And it is shown that finding the independence number andindependent domination number of a given graph of 64 vertices areequivalent to finding respectively the maximum number of Queenswhich control each square and the minimum number of attackingQueens and non-attacking Queens on a8 x 8 chessboard