## Description

A method for characterizing graphs that have smallest (or largest)Laplacian eigenvalue within a particular class of graphs works as

following:

Take a Perron vector, rearrange the edges of the graph and compare the

respective Rayleigh quotients. By the Rayleigh-Ritz Theorem we can draw some conclusions about the change of the smallest eigenvalue. This approach, however, does not work for the k-th Laplacian eigenvalue, as now we have to use the Courant-Fisher

Theorem that involves minimization of the Rayleigh quotients with respect to constraints that are hard to control.

In this talk we show that sometimes we can get local properties of

extremal graphs by means of the concept of "geometric nodal domains"

and "Dirichlet matrices". This is in particular the case for the algebraic connectivity.

Period | 1 Jul 2009 |
---|---|

Event title | 24th LL-Seminar on Graph Theory |

Event type | Unkonwn |

Degree of Recognition | National |