OFFSET

1,2

COMMENTS

LINKS

R. Grone and R. Merris, Indecomposable Laplacian integral graphs, Linear Algebra and its Applications, 428 (2008), 1565-1570.

EXAMPLE

For n <= 3, all graphs are Laplacian integral, so a(n) = A000088(n) when n <= 3.

There is exactly one graph on 4 vertices that is not Laplacian integral: the path P_4, which has Laplacian matrix

1 -1 0 0

-1 2 -1 0

0 -1 2 -1

0 0 -1 1

which has eigenvalues 0, 2, 2-sqrt(2), and 2+sqrt(2), which are not all integers.

CROSSREFS

KEYWORD

nonn,more

AUTHOR

Nathaniel Johnston, May 16 2023

EXTENSIONS

a(10) from M. A. Achterberg, May 26 2023

STATUS

approved