5 The Problems and Answers of the Graphs.

These boards are not as beautiful as the graphs we have presented, but these boards have interesting patterns. These boards show the structures of the graphs.

Graph 1.

[Graphics:HTMLFiles/board_1.gif]

Graph 2.

[Graphics:HTMLFiles/board_2.gif]

Graph 3.

[Graphics:HTMLFiles/board_3.gif]

There is a Hamiltonian circuit in Graph 3.

Graph 4.

[Graphics:HTMLFiles/board_4.gif]

There is a Hamiltonian circuit in Graph 4.

Graph 5.

[Graphics:HTMLFiles/board_5.gif]

Graph 6.

[Graphics:HTMLFiles/board_6.gif]

There is a Hamiltonian circuit in Graph 6.

Graph 7.

[Graphics:HTMLFiles/board_7.gif]

There is a Hamiltonian circuit in Graph 7.

Graph 8.

[Graphics:HTMLFiles/board_8.gif]

Graph 9.

[Graphics:HTMLFiles/board_9.gif]

There is a Hamiltonian circuit in Graph 9.

Graph 10.

[Graphics:HTMLFiles/board_11.gif]

The following problems are  disjoint unions of two Knight's Tours.

Graph 11.

[Graphics:HTMLFiles/board_12.gif]

Graph 12.

[Graphics:HTMLFiles/board_13.gif]

Graph 13.

[Graphics:HTMLFiles/board_14.gif]

If you are interested in making a beautiful graph, it is important to use computer graphics. We used Mathematica to produce these graphics.

Go back to Section 1.

Go to Section 2 "A Gallery of Graphs Part 1".

Go to Section 3 "A Gallery of Graphs Part 2".

Go to Section 4 "A Gallery of Graphs part 3".