Document Type
Article
Department/Program
Mathematics
Journal Title
Discrete Mathematics
Pub Date
2011
Volume
311
Issue
3-Feb
First Page
166
Abstract
When an edge is removed from an undirected graph, there is a limited change that can occur in the multiplicity of an eigenvalue of a Hermitian matrix with that graph. Primarily for trees, we identify the changes that can occur and characterize the circumstances under which they occur. This extends known results for the removal of vertices. A catalog of examples is given to illustrate the possibilities that can occur and to contrast the case of trees with that of general graphs. (C) 2010 Elsevier B.V. All rights reserved.
Recommended Citation
McMichael, Paul R. and Johnson, Charles R., The change in multiplicity of an eigenvalue of a Hermitian matrix associated with the removal of an edge from its graph (2011). Discrete Mathematics, 311(3-Feb), 166-170.
10.1016/j.disc.2010.10.010
DOI
10.1016/j.disc.2010.10.010
