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Spectra of weighted compound graphs of generalized Bethe trees

Spectra of weighted compound graphs of generalized Bethe trees

A generalized Bethe tree is a rooted tree in which vertices at the same distance from the root have the same degree. Let Gm be a connected weighted graph on m vertices. Let {Bi :1≤ i ≤ m} be a set of trees such that, for i =1 ,2,...,m , …