A006608 Number of n-node graphs not determined by their spectrum. (Formerly M1981)

0, 0, 0, 0, 2, 10, 110, 1722, 51039, 2560606, 215331676, 31067572481

Offset

1,5

References

N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

Links

Table of n, a(n) for n=1..12.

Andries E. Brouwer, Numbers of characteristic polynomials and cospectral graphs for A

A. E. Brouwer and E. Spence, Cospectral graphs on 12 vertices, Electr. J. Combin. 16 (2009) N20. (p. 199).

C. Godsil and B. D. McKay, Some computational results on the spectra of graphs, pp. 73-92 of Combinatorial Mathematics IV (Adelaide 1975), Lect. Notes Math., 560 (1976).

Andreas Holmstrom, A first step towards automated conjecture-making in higher arithmetic geometry, Work-in-progress paper presented at the Conference on Intelligent Computer Mathematics, July 2016. Published in the CEUR Workshop Proceedings.

Jürgen Jost, Raffaella Mulas, and Leo Torres, Spectral theory of the non-backtracking Laplacian for graphs, arXiv:2203.10824 [math.SP], 2022.

P. W. Mills, R. P. Rundle, J. H. Samson, Simon J. Devitt, Todd Tilma, V. M. Dwyer, and Mark J. Everitt, Quantum invariants and the graph isomorphism problem, Phys. Rev. A 100, 052317 (2019).

E. Spence, Numbers of characteristic polynomials and cospectral graphs for A

Eric Weisstein's World of Mathematics, Cospectral Graphs

Eric Weisstein's World of Mathematics, Determined by Spectrum

Crossrefs

Cf. A178925 (simple graphs determined by spectrum), A099881, A099882.

Sequence in context: A062412 A212491 A364409 * A066205 A113147 A335946

Adjacent sequences: A006605 A006606 A006607 * A006609 A006610 A006611

Keyword

nonn,hard,more

Author

N. J. A. Sloane

Extensions

a(10) from Eric W. Weisstein, Dec 30 2010

Two more terms from Ruperto Corso, Dec 18 2011

Status

approved