Structure of Trees with Respect to Nodal Vertex Sets

07/28/2019

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by   Asghar Bahmani, et al.

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Let T be a tree with a given adjacency eigenvalue λ. In this paper, by using the λ-minimal trees, we determine the structure of trees with a given multiplicity of the eigenvalue λ. Furthermore, we consider the relationship between the structure of trees and the eigensystem of a given Laplacian eigenvalue.