The inverse characteristic polynomial problem for trees (Q1980921)

The authors are interested in understanding which real polynomials occur as characteristic polynomials of real matrices for a given tree. For a tree \(T\), let \(\mathcal{R}(T)\) denote the set of real matrices whose graph is \(T\). A constructive method (see Theorem 3.5) is provided: for each tree it provides many characteristic polynomials from \(\mathcal{R}(T)\), and for many trees (paths and trees with fewer than ten vertices) gives all of them. For the entire collection see [Zbl 1471.47002].