A242952 Number of connected graphs on n vertices whose spectrum has n distinct eigenvalues.

1, 1, 1, 3, 11, 54, 539, 7319, 209471, 10000304

Offset

1,4

Comments

The spectrum refers to the eigenvalues of the adjacency matrix.

Links

Table of n, a(n) for n=1..10.

Travis Hoppe and Anna Petrone, Encyclopedia of Finite Graphs

Travis Hoppe and Anna Petrone, Integer sequence discovery from small graphs, arXiv preprint arXiv:1408.3644 [math.CO], 2014.

Haiying Shan and Xiaoqi Liu, Exploring Graphs with Distinct M-Eigenvalues: Product Operation, Wronskian Vertices, and Controllability, arXiv:2412.18759 [math.CO], 2024. See pp. 14-15.

Eric Weisstein's World of Mathematics, Graph Spectrum

Crossrefs

Cf. A064731 (integral graphs), A242953 (non-distinct spectrum graphs).

Sequence in context: A267832 A095707 A259105 * A266027 A306177 A377965

Adjacent sequences: A242949 A242950 A242951 * A242953 A242954 A242955

Keyword

nonn,more,changed

Author

Travis Hoppe and Anna Petrone, May 27 2014

Extensions

Corrected, original description as the "real spectrum" was incorrect, by Travis Hoppe, Mar 23 2015

Status

approved