The Graphs for which the Maximum Multiplicity of an Eigenvalue is Two

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Characterized are all simple undirected graphs $G$ such that any real symmetric matrix that has graph $G$ has no eigenvalues of multiplicity more than 2. All such graphs are partial 2-trees (and this follows from a result for rather general fields), but only certain partial 2-trees guarantee maximum multiplicity 2. Among partial linear 2-trees, they are only those whose vertices can be covered by two "parallel" induced paths. The remaining graphs that guarantee maximum multiplicity 2 are comprised by certain identified families of "exceptional" partial 2-trees that are not linear.

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Combinatorics, 05C50; 15A57

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http://salesiana.dossiersoluciones.com/handle/123456789/122407

Consulte el texto completo en el siguiente enlace:

https://arxiv.org/abs/math/0701562
 http://arxiv.org/abs/math/0701562

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arXiv