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1. Applications of recurrence relations for the characteristic polynomials of Bethe trees

Author

Robbiano, María and Trevisan, Vilmar

Subjects
*POINT mappings (Mathematics), *POLYNOMIALS, *TREE graphs, *TOPOLOGICAL degree, *INVARIANTS (Mathematics), *MATHEMATICAL analysis
Abstract

Abstract: A Bethe tree of levels, , is a rooted tree such that the root vertex has degree , the vertices from level to have degree and the vertices at level are leaves. In this paper, we obtain a recurrence relation for the characteristic polynomial and the Laplacian characteristic polynomial of Bethe trees. As an application, we prove that there are no integral Bethe trees except for the star , and we obtain a recurrence relation for the Laplacian-energy-like invariant of Bethe trees. [Copyright &y& Elsevier]

Published
2010
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