In chess, a knight can move in any direction, but it must move two spaces then turn and move one more space. The eight possible moves a knight can make from a space in the center of a five-by-five grid are shown in the first figure. Draw a graph that represents all the legal moves of a knight on a three-by-three grid starting from the lower left corner as shown in the second figure where the vertices will represent the spaces occupied by the knight and the edges will indicate a move from one space to the next.