Titlebook: Locating Eigenvalues in Graphs; Algorithms and Appli Carlos Hoppen,David P. Jacobs,Vilmar Trevisan Book 2022 The Editor(s) (if applicable)

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Locating Eigenvalues Using Tree Decomposition,The aim of this chapter is to introduce an eigenvalue location algorithm for a symmetric matrix . that uses a nice tree decomposition associated with its underlying graph. The algorithm is linear time for graphs with bounded width, assuming that the tree decomposition is part of the input.

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Graph Classes and Graph Decompositions,rticular, we shall discuss the class of cographs and its characterizations. We shall also present tree decompositions and clique decompositions of graphs. This is related to ., which has many important algorithmic implications.

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https://doi.org/10.1007/978-3-031-11698-8spectrum; linear-time algorithm; graph; adjacency matrix; Laplacian matrix; tree; spectral graph theory; ei

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