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

Subject Areas : Applied Mathematics Modeling

Abbas Heydari ^{1 *}

1 - Arak University of Technology, Daneshgah St., Arak, Iran. Post Code: 38181-41167

Received: 2022-02-07 Accepted : 2022-03-01 Published : 2020-05-01

Keywords: Laplacian matrix, adjacency matrix, Characteristic polynomial, Tree,

Abstract :

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.