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Some spectral properties of starlike trees. (English) Zbl 0997.05059

A tree in which exactly one vertex has degree greater than two is said to be starlike. The authors prove that at most one eigenvalue of a starlike tree is greater than two. Starlike trees which do not have an eigenvalue greater than two are easily identified using a known enumeration of graphs in which the largest eigenvalue does not exceed two. They derive an upper and a lower bound for the largest eigenvalue of a starlike tree.

MSC:

05C50 Graphs and linear algebra (matrices, eigenvalues, etc.)
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