Abstract
The notion of the Laplacian of weighted graphs will be introduced, the eigenvectors belonging to k consecutive eigen-values of which define optimal k-dimensional Euclidean representation of the vertices. By means of these spectral techniques some combinatorial problems concerning minimal ( k+1)-cuts of weighted graphs can be handled easily with linear algebraic tools. (Here k is an arbitrary integer between 1 and the number of vertices.) The ( k+1)-variance of the optimal k-dimensional representatives is estimated from above by the k smallest positive eigenvalues and by the gap in the spectrum between the kth and ( k+1)th positive eigenvalues in increasing order.
Sign-in/Register to access full text options 
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.
