Getting from 1 point to another in less than 3 moves!!

When trying to find if you can get from one vertex to another in 3 or less moves you can find it out with matrix algetbra. Here is a 10×10 matrix that can get from anypoint to anypoint in 3 or less moves.

A+A^2+A^3

A= 0 1 0 0 1 0 0 1 0 0
1 0 0 1 0 0 1 0 0 0
0 0 0 1 0 0 1 0 0 1
0 1 1 0 0 0 0 1 0 0
1 0 0 0 0 1 0 0 1 0
0 0 0 0 1 0 0 1 1 0
0 1 1 0 0 0 0 0 0 1
1 0 0 1 0 1 0 0 0 0
0 0 0 0 1 1 0 0 0 1
0 0 1 0 0 0 1 0 1 0
A^2

3 0 0 2 0 2 1 0 1 0
0 3 2 0 1 0 0 2 0 1
0 2 3 0 0 0 1 1 1 1
2 0 0 3 0 1 2 0 0 1
0 1 0 0 3 1 0 2 1 1
2 0 0 1 1 3 0 0 1 1
1 0 1 2 0 0 3 0 1 1
0 2 1 0 2 0 0 3 1 0
1 0 1 0 1 1 1 1 3 0
0 1 1 1 1 1 1 0 0 3
A^3
0 6 3 0 6 1 0 7 2 2
6 0 1 7 0 3 6 0 2 2
3 1 2 6 1 2 6 0 1 5
0 7 6 0 3 0 1 6 2 2
6 0 1 3 2 6 2 1 5 1
1 3 2 0 6 2 1 6 5 1
0 6 6 1 2 1 2 3 1 5
7 0 0 6 1 6 3 0 2 2
2 2 1 2 5 5 1 2 2 5
2 2 5 2 1 1 5 2 5 2
A^2+A^3=
3 6 3 2 6 3 1 7 3 2
6 3 3 7 1 3 6 2 2 3
3 3 5 6 1 2 7 1 2 6
2 7 6 3 3 1 3 6 2 3
6 1 1 3 5 7 2 3 6 2
3 3 2 1 7 5 1 6 6 2
1 6 7 3 2 1 5 3 2 6
7 2 1 6 3 6 3 3 3 2
3 2 2 2 6 6 2 3 5 5
2 3 6 3 2 2 6 2 5 5

The matrix A represents the line graph that each vertex has 3 lines coming off it. A tells you how many ways of walk 1 from each vertex to another

~ by mathwizhoax on December 11, 2008.