Abstract
Let A be the adjacency matrix of a connected graph G . If z is a column vector, we say that a vertex of G is positive, nonnegative, null, etc. if the corresponding entry of z has that property. For z such that Az⩾ az, we bound the number of components in the subgraph included by positive vertices. For eigenvectors z having a null element, we bound the number of components in the graph included by nonnull vertices. Finally, bounds are established for the number of null elements in an eigenvector, for the multiplicity of an eigenvalue and for the magnitudes of the second and last eigenvalues of a general or a bipartite graph.
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
