We display the polynomials in the form of a matrix. The entry in position

The cycle of length four. Tutte Polynomial,

0 1 1 1 1This represents the polynomial

Rank Polynomial,

4 1 6 4 1

Rank Polynomial,

1 0 4 0 6 0 4 1

The above example demonstrates (in a small way) that the coefficients of the Tutte Polynomial are smaller than the coefficients of the Rank Polynomial. For these remaining examples, we display only the Tutte Polynomial.

The complete graph on one vertex.

1

The complete graph on two vertices.

0 1

The complete graph on three vertices.

0 1 1 1

The complete graph on four vertices.

0 2 3 1 2 4 3 1When the graph is self dual, the matrix is symmetric.

The complete graph on five vertices.

0 6 15 15 10 4 1 6 20 15 5 11 10 6 1

The complete graph on six vertices.

0 24 80 120 120 96 64 35 15 5 1 24 106 145 105 60 24 6 50 90 45 15 35 20 10 1

The complete graph on seven vertices.

0 120 490 945 1225 1260 1120 895 645 420 245 126 56 21 6 1 120 644 1225 1330 1085 756 469 245 105 35 7 274 721 700 420 210 84 21 225 280 105 35 85 35 15 1

The Petersen graph.

0 36 84 75 35 9 1 36 168 171 65 10 120 240 105 15 180 170 30 170 70 114 12 56 21 6 1

maple has a function called tuttepoly in the networks package.

Last modified January 23, 1996, by S.C. Locke. How to contact me.