I am wondering if there exists two graphs, which are not isomorphic with the condition that both of them have the same spectrum.
Two graphs are isomorphic when they may be drawn in the same way.
Spectrum I mean set of all eigenvalues of the matrix of the graph.
https://en.wikipedia.org/wiki/Spectrum_of_a_matrix
Anybody may give me hint or some suggestions ? Or maybe this problem is already solved in math ?
I have seen the closiest topic to mine: Given two non-isomorphic graphs with the same number of edges, vertices and degree, what is the most efficient way of proving they are not isomorphic?, however it is not direct answer to mine wonders, since the eigenvalues may be different in those graphs if I am correct.