A243048 Number of simple graphs on n nodes having a non-unique Tutte polynomial.

0, 0, 0, 4, 15, 84, 548, 5629, 90776, 2493299

Offset: 1

Author

Eric W. Weisstein, May 29 2014

Keywords

• nonn
• hard
• more

Comments

Graphs on different numbers of nodes can have identical Tutte polynomials; the numbers here represent counts of non-unique polynomials among other n-node graphs only.

Examples

			On 4 nodes,
  P_3 \cup K_1 and 2P_2 both have Tutte polynomial x^2
  P_4 and K_1,3 both have Tutte polynomial x^3
so there are a(4) = 2 + 2 = 4 graphs with non-unique Tutte polynomials.
		

Links

• Eric Weisstein's World of Mathematics, Tutte Polynomial

Crossrefs

Cf. A243049 (number of Tutte-unique graphs).

Cf. A000088 (number of simple graphs on n nodes).

Formula

a(n) = A000088(n) - A243049(n).

Extensions

a(10) from Eric W. Weisstein, Jun 09 2014