Tight bounds on the algebraic connectivity of a balanced binary tree.

Molitierno, Jason J.; Neumann, Michael; Shader, Bryan L.

Displaying similar documents to “Tight bounds on the algebraic connectivity of a balanced binary tree.”

On two conjectures regarding an inverse eigenvalue problem for acyclic symmetric matrices.

Barioli, Franceso, Fallat, Shaun M. (2004)

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The third smallest eigenvalue of the Laplacian matrix.

Pati, Sukanta (2001)

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Note on deleting a vertex and weak interlacing of the Laplacian spectrum.

Lotker, Zvi (2007)

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The number of eigenvalues greater than two in the Laplacian spectrum of a graph

Merris, Russell (1991)

Portugaliae mathematica

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Extremal algebraic connectivities of certain caterpillar classes and symmetric caterpillars.

Rojo, Oscar, Medina, Luis, De Abreu, Nair M.M., Justel, Claudia (2010)

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Spectral graph theory and the inverse eigenvalue problem of a graph.

Hogben, Leslie (2005)

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Bounds on the subdominant eigenvalue involving group inverses with applications to graphs

Stephen J. Kirkland, Neumann, Michael, Bryan L. Shader (1998)

Czechoslovak Mathematical Journal

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Let $A$ be an $n \times n$ symmetric, irreducible, and nonnegative matrix whose eigenvalues are $λ_{1} > λ_{2} \geq ... \geq λ_{n}$ . In this paper we derive several lower and upper bounds, in particular on $λ_{2}$ and $λ_{n}$ , but also, indirectly, on $μ = {max}_{2 \leq i \leq n} | λ_{i} |$ . The bounds are in terms of the diagonal entries of the group generalized inverse, $Q^{#}$ , of the singular and irreducible M-matrix $Q = λ_{1} I - A$ . Our starting point is a spectral resolution for $Q^{#}$ . We consider the case of equality in some of these inequalities and we apply our results to the algebraic connectivity...

On Cayley's formula for counting trees in nested interval graphs.

Coppersmith, Don, Lotker, Zvi (2004)

ELA. The Electronic Journal of Linear Algebra [electronic only]

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A lower bound for the number of distinct eigenvalues of some real symmetric matrices.

Da Fonseca, C.M. (2010)

ELA. The Electronic Journal of Linear Algebra [electronic only]

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Limit points for normalized Laplacian eigenvalues.

Kirkland, Steve (2006)

ELA. The Electronic Journal of Linear Algebra [electronic only]

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