Line Graph Analysis of Mazes/Labyrinth

Your Name: _______________________________________

Names of Other Group Members:_______________________

Name of Maze/Labyrinth: _____________________________

A maze is a complex branching (multicursal) puzzle that includes choices of path and direction, may have multiple entrances and exits, and dead ends.

A labyrinth is unicursal i.e. has only a single, non-branching path, which leads to the center then back out the same way, with only one entry/exit point.

Purpose:

To represent a maze/labyrinth to better understand line graph theory. To analyze a maze/labyrinth according to line graph theory.

Tasks:

Create a maze or labyrinth. Draw the paths that take you through the maze successfully. Any alternate path ways must be drawn in another colour. Minimize the number of colours used for the various paths, so that no two paths of the

same colour touch. Label each junction of the path by a letter of the alphabet starting at A. Put arrows on the path to indicate the direction to follow.

Analysis:

On an 8”x11” sheet of paper, represent the maze by simplifying the paths through the maze.

Determine the number of nodes and the degree of each nodes. Determine the chromatic number for your maze.

Characteristic:Determine the following:

Response and Justification.

1. The order of your graph.

2. The highest degree of a vertex in your graph.

3. Does your graph contain a loop?

4. Name a pair of adjacent vertices.

5. Name a pair of parallel edges.

6. Is the graph connected?

7. Is the graph complete?

8. The distance of the path from the start to the end of the maze/labyrinth.

9. Is the Q. 8 path a simple path?

10. Number of vertices of even degree.

11. Number of vertices of odd degree.

12. Is the Q. 8 path an Euler path?

13. Is the Q.8 path a Hamiltonian path?

14. Is the Q.8 path a directed path?

15. Is the graph a tree?

16. What is the chromatic number of your graph?

17. Colour your line graph accordingly.