Chapter 10.5, Problem 57E

A knightis a chess piece that can move either two spaces horizontally and one space vertically or one space horizontally and two spaces vertically. That is, a knight on square (x, y) can move to any of the eight squares (x ± 2, y ± 1), (x ± 1,y ± 2), if these squares are on the chessboard, as illustrated here.

Aknight's touris a sequence of legal moves by a knight starting at some square and visiting each square exactly once. A knight's tour is calledreentrantif there is a legal move that takes the knight from the last square of the tour back to where the tour began. We can model knight's tours using the graph that has a vertex for each square on the board, with an edge connecting two vertices if a knight can legally move between the squares represented by these vertices.

Draw the graph that represents the legal moves of a knight on a 3??4 chessboard.