Abstract In this paper we introduce modular knight distance on a chessboard and use it to study the geometry of a class of solutions of the (modular) n -queens problem. Such geometry is related to the movement of a knight in classic chess, therefore we benefit from defining modular knight distance prior to the study. The concept of the distance is incorporated to graph theory with the notion of the knight graph, from which we obtain several properties which allows us to study the desired class of solutions. In the end of the study we obtain an algorithm with relatively reduced complexity which can be used to generate all the solutions of the class. The idea of such algorithm can be used for computing all the solutions of broader classes. Additionally we prove a result about the analytical classification of all the solutions of the class in interest.

中文翻译：

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图中的模块化骑士距离及其在 n-皇后问题上的应用

摘要 在本文中，我们介绍了棋盘上的模骑士距离，并用它来研究（模）n-皇后问题的一类解的几何。这种几何形状与经典国际象棋中骑士的移动有关，因此我们受益于在研究之前定义模块化骑士距离。距离的概念与骑士图的概念结合到图论中，我们从中获得了几个属性，使我们能够研究所需的解决方案类别。在研究的最后，我们得到了一个复杂度相对降低的算法，可以用来生成该类的所有解。这种算法的思想可以用于计算更广泛的类的所有解决方案。