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

الموضوعات :

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

تاريخ الإرسال : 06 الإثنين , رجب, 1443 تاريخ التأكيد : 28 الثلاثاء , رجب, 1443 تاريخ الإصدار : 08 الجمعة , رمضان, 1441

الکلمات المفتاحية: Laplacian matrix, adjacency matrix, Characteristic polynomial, Tree,

ملخص المقالة :

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.