N ov 2 01 6 Constructions of Graphs and Trees with Partially Prescribed Spectrum ∗
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چکیده
It is shown how a connected graph and a tree with partially prescribed spectrum can be constructed. These constructions are based on a recent result of Salez that every totally real algebraic integer is an eigenvalue of a tree. This implies that for any (not necessarily connected) graph G, there is a tree T such that the characteristic polynomial P (G, x) of G can divide the characteristic polynomial P (T, x) of T , i.e., P (G, x) is a divisor of P (T, x).
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تاریخ انتشار 2016