The spectrum of the Laplacian matrix of a balanced binary tree
Copyright policy )The spectrum of the Laplacian matrix of a balanced binary tree
Let \(L({\mathcal B}_k)\) be the Laplacian matrix of an unweighted balanced binary tree \({\mathcal B}_k\) of \(k\) levels. The author completely characterizes the eigenvalues of \(L({\mathcal B}_k)\) by labelling vertices of \({\mathcal B}_k\) in such a way that \(L({\mathcal B}_k)\) becomes a symmetric persymmetric matrix.
Numerical Analysis, Eigenvalues, singular values, and eigenvectors, Algebra and Number Theory, Graphs and linear algebra (matrices, eigenvalues, etc.), Binary trees, Algebraic connectivity, Trees, Discrete Mathematics and Combinatorics, Laplacian eigenvalues, Geometry and Topology, balanced binary tree, Laplacian matrix
Numerical Analysis, Eigenvalues, singular values, and eigenvectors, Algebra and Number Theory, Graphs and linear algebra (matrices, eigenvalues, etc.), Binary trees, Algebraic connectivity, Trees, Discrete Mathematics and Combinatorics, Laplacian eigenvalues, Geometry and Topology, balanced binary tree, Laplacian matrix
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