Article ID Journal Published Year Pages File Type
4602201 Linear Algebra and its Applications 2009 21 Pages PDF
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.

Related Topics
Physical Sciences and Engineering Mathematics Algebra and Number Theory