Integer valued eigenvalues

asked 2024-03-13 13:05:32 +0100

Anonymous

updated 2024-03-13 20:55:55 +0100

for G in graphs.nauty_geng("8 -c"):
    A=G.adjacency_matrix().eigenvalues()
    L=G.laplacian_matrix().eigenvalues()
    show(A,L)
    G.show()

Using the above code, I have obtained the all possible eigenvalues of the adjacency and Laplacian matrix. But I need only those graphs for which the adjacency and laplacian matrices have all integer eigenvalues. How to collect only the integer eigenvalues from this large collection?

answered 2024-03-13 19:39:57 +0100

Max Alekseyev

6488 ●9 ●47 ●153

updated 2024-03-13 21:38:08 +0100

Integer eigen values can be obtained with .charpoly().roots(ZZ) instead of .eigenvalues(). Correspondingly, the graphs you look for, can be obtained as

n = 8
for G in graphs.nauty_geng(f"{n} -c"):
    if sum(m for _,m in G.adjacency_matrix().charpoly().roots(ZZ))==n and sum(m for _,m in G.laplacian_matrix().charpoly().roots(ZZ))==n:
        G.show()

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Comments

But it is not coming the correct answer.

rewi ( 2024-03-13 20:52:41 +0100 )edit

What do you mean? What is "correct answer"?

Max Alekseyev ( 2024-03-13 21:20:56 +0100 )edit

I need only those graphs whose adjacency as well as laplacian matrices have all eigenvalues integers. but the code after modification, as you suggested still giving graphs which do not have integer eigenvalues. Some extra graphs are coming. we have to exclude those graphs

rewi ( 2024-03-13 21:28:19 +0100 )edit

@rewi: I've added a complete code.

Max Alekseyev ( 2024-03-13 21:38:25 +0100 )edit

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