Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
4602201 | Linear Algebra and its Applications | 2009 | 21 Pages |
Abstract
A generalized Bethe tree is a rooted tree in which vertices at the same distance from the root have the same degree. Let Pm be a path of m vertices. Let {Bi:1⩽i⩽m} be a set of generalized Bethe trees. Let Pm{Bi:1⩽i⩽m} be the tree obtained from Pm and the trees B1,B2,…,Bm by identifying the root vertex of Bi with the i-th vertex of Pm. We give a complete characterization of the eigenvalues of the Laplacian and adjacency matrices of Pm{Bi:1⩽i⩽m}. In particular, we characterize their spectral radii and the algebraic conectivity. Moreover, we derive results concerning their multiplicities. Finally, we apply the results to the case B1=B2=…=Bm.
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