A243049 -id:A243049 - cp's OEIS frontend

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

Eric W. Weisstein, May 29 2014

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.

			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.

Eric Weisstein's World of Mathematics, Tutte Polynomial

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

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

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

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

A245881 Number of distinct Tutte polynomials among all connected graphs on n nodes.

Original entry on oeis.org

1, 1, 2, 5, 16, 73, 532, 7245, 192605, 9717156

Offset: 1

Travis Hoppe and Anna Petrone, Aug 05 2014

Travis Hoppe and Anna Petrone, Encyclopedia of Finite Graphs
T. Hoppe and A. Petrone, Integer sequence discovery from small graphs, arXiv preprint arXiv:1408.3644 [math.CO], 2014.
T. Hoppe and A. Petrone, Integer sequence discovery from small graphs, Discr. Appl. Math. 201 (2016) 172-181.
Eric Weisstein's World of Mathematics, Tutte Polynomial

Cf. A243049 (simple graphs, including disconnected ones, with unique Tutte polynomials).

Terms corrected by Eric M. Schmidt, Mar 20 2015

cp's OEIS Frontend

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

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