Starlike tree

In the area of mathematics known as graph theory, a tree is said to be starlike if it has exactly one vertex of degree greater than 2. This high-degree vertex is the root and a starlike tree is obtained by attaching at least three linear graphs to this central vertex.

A starlike tree

Properties

Two finite starlike trees are isospectral, i.e. their graph Laplacians have the same spectra, if and only if they are isomorphic.^[1] The graph Laplacian has always only one eigenvalue equal or greater than 4.^[2]