In computer science diagrams like this are often used to represent the essential information of a problem. Such a diagram is called a graph. The circles in the diagram are called vertices or nodes of the graph.In a graph it is only important whether two vertices are connected or not. Where the vertices are drawn is immaterial. The same graph can often be drawn in different ways, as is illustrated in the explanation section: Both answer A and the last picture in the explanation are correct diagrams for the board and represent the same graph.Whether a graph can be a useful representation of a computer science problem depends on what information you need to solve the problem. If, for instance, you need to know whether a white piece on the board is in the same row or column as a black piece, then our graphs are not a good representations: The colour of the pieces is not represented in the nodes. If you need to know whether there are sufficient pieces left on the board so that a game can still be won, then a graph is 'overkill': You only need to keep track of how many pieces are left on the board at each moment, and there is no need to record which piece is in the same row or column as another piece. On the other hand, the graph is a good representation for answering questions such as: 'What is the minimal number of pieces you have to remove so that no piece is in the same column or row as any other piece?'Finding the correct representation for a problem is one of the challenges a programmer or computer scientist encounters regularly in their job.