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Does there exists any simple connected graph G of order n, such that whenever λk is an eigenvalue of the adjacency matrix of G

Does there exists any simple connected graph G of order n, such that whenever λk is an eigenvalue of the adjacency matrix of G, kλ is also an eigenvalue of adjacency matrix of G. Here k is any positive natural number (k=1,2,3,4,5,) and λ(0) is an eigenvalue of adjacency matrix of G.

Can any one help me with a SAGE code.

Does there exists any simple connected graph G of order n, such that whenever λk is an eigenvalue of the adjacency matrix of G

Does there exists any simple connected graph G of order n, such that whenever λk is an eigenvalue of the adjacency matrix of G, kλ is also an eigenvalue of adjacency matrix of G. Here k is any positive natural number (k=1,2,3,4,5,) and λ(0) is an eigenvalue of adjacency matrix of G.

Can any one help me with a SAGE code.code. (Also ( kλ, λk)) should have same multiplicity

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Does there exists any simple connected graph G of order n, such that whenever λk is an eigenvalue of the adjacency matrix of G

Does there exists any simple connected graph G of order n, such that whenever λk is an eigenvalue of the adjacency matrix of G, kλ is also an eigenvalue of adjacency matrix of G. Here k is any positive natural number (k=1,2,3,4,5,) and λ(0) is an eigenvalue of adjacency matrix of G.

Can any one help me with a SAGE code. (Also ( kλ, λk)) should have same multiplicity