The Graphs for which the Maximum Multiplicity of an Eigenvalue is Two
Combinatorics
2007-05-23 v1
Abstract
Characterized are all simple undirected graphs such that any real symmetric matrix that has graph 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.
Keywords
Cite
@article{arxiv.math/0701562,
title = {The Graphs for which the Maximum Multiplicity of an Eigenvalue is Two},
author = {Charles R. Johnson and Raphael Loewy and Paul Anthony Smith},
journal= {arXiv preprint arXiv:math/0701562},
year = {2007}
}