Displaying similar documents to “On the coefficients of the Laplacian characteristic polynomial of trees.”

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

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....