On the computation of characteristic polynomials and spectra of balanced rooted trees

A generalized Bethe tree is a rooted unweighted tree in whichthe vertices in each of its levels have equal degree. In this paperwe derive an explicit formula for the characteristic polynomialsof the adjacency and Laplacian matrices of unweighted rootedtree which obtained from the union of the generalized Bethe treesjoined at their respective root vertices by using of rooted productof graphs.

کلیدواژه ها:

Characteristic polynomial ، Tree ، adjacency matrix ، Laplacian matrix