Problems
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By (10) they occur in inverse pairs, with 1 an eigenvalue for all odd n; how big is the largest?
Another problem worth mentioning is whether the lower bound for c_2(G) still holds without the regularity assumptions, i.e. if we only assume that the graph has large girth and the degree of each vertex is greater than 2.
There exists t_0 ∈ N such that m_G_t(-∞, -2) is constant for all t ≥ t_0.