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

Theory of Approximation and Applications

مقاله 7، دوره 14، شماره 1، مرداد 2020، صفحه 89-96   

نوع مقاله: Research Articles

نویسنده

Abbas Heydari^*

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

چکیده

A generalized Bethe tree is a rooted unweighted tree in which
the vertices in each of its levels have equal degree. In this paper
we derive an explicit formula for the characteristic polynomials
of the adjacency and Laplacian matrices of unweighted rooted
tree which obtained from the union of the generalized Bethe trees
joined at their respective root vertices by using of rooted product
of graphs.

کلیدواژه‌ها

Characteristic polynomial؛ Tree؛ Adjacency matrix؛ Laplacian matrix