Displaying similar documents to “Laplacian matrix and distance in trees”

The maximum multiplicity and the two largest multiplicities of eigenvalues in a Hermitian matrix whose graph is a tree

Rosário Fernandes (2015)

Special Matrices

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The maximum multiplicity of an eigenvalue in a matrix whose graph is a tree, M1, was understood fully (froma combinatorial perspective) by C.R. Johnson, A. Leal-Duarte (Linear Algebra and Multilinear Algebra 46 (1999) 139-144). Among the possible multiplicity lists for the eigenvalues of Hermitian matrices whose graph is a tree, we focus upon M2, the maximum value of the sum of the two largest multiplicities when the largest multiplicity is M1. Upper and lower bounds are given for M2....

Helly Property for Subtrees

Jessica Enright, Piotr Rudnicki (2008)

Formalized Mathematics

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We prove, following [5, p. 92], that any family of subtrees of a finite tree satisfies the Helly property.MML identifier: HELLY, version: 7.8.09 4.97.1001

Constructions for type I trees with nonisomorphic Perron branches

Stephen J. Kirkland (1999)

Czechoslovak Mathematical Journal

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A tree is classified as being type I provided that there are two or more Perron branches at its characteristic vertex. The question arises as to how one might construct such a tree in which the Perron branches at the characteristic vertex are not isomorphic. Motivated by an example of Grone and Merris, we produce a large class of such trees, and show how to construct others from them. We also investigate some of the properties of a subclass of these trees. Throughout, we exploit connections...