This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A363065 #14 May 26 2023 11:29:22 %S A363065 1,2,4,10,24,70,188,553,1721,5716 %N A363065 Number of Laplacian integral graphs on n vertices. %C A363065 A (simple, undirected) graph is called Laplacian integral if all eigenvalues of its Laplacian matrix are integers. The corresponding sequence that uses the adjacency matrix instead of the Laplacian matrix is A077027. %C A363065 Since every cograph is Laplacian integral, a(n) >= A000084(n). %H A363065 R. Grone and R. Merris, <a href="https://doi.org/10.1016/j.laa.2007.09.025">Indecomposable Laplacian integral graphs</a>, Linear Algebra and its Applications, 428 (2008), 1565-1570. %e A363065 For n <= 3, all graphs are Laplacian integral, so a(n) = A000088(n) when n <= 3. %e A363065 There is exactly one graph on 4 vertices that is not Laplacian integral: the path P_4, which has Laplacian matrix %e A363065 1 -1 0 0 %e A363065 -1 2 -1 0 %e A363065 0 -1 2 -1 %e A363065 0 0 -1 1 %e A363065 which has eigenvalues 0, 2, 2-sqrt(2), and 2+sqrt(2), which are not all integers. %Y A363065 Cf. A000084, A000088, A077027, A363064 (connected graphs only). %K A363065 nonn,more %O A363065 1,2 %A A363065 _Nathaniel Johnston_, May 16 2023 %E A363065 a(10) from _M. A. Achterberg_, May 26 2023