欢迎光临!
您现在所在的位置:首页 >> 通知公告 & 学术信息
学术信息
SEMINARS
The Colin de Verdiere number of split graphs
时间  Datetime
2017-09-05 15:30 — 17:00 
地点  Venue
Middle Lecture Room
报告人  Speaker
Abraham Berman
单位  Affiliation
Technion - Israel Institute of Technology
邀请人  Host
张晓东
报告摘要  Abstract

A CdV matrix of a graph G is a generalized Laplacian matrix of G that has 1 negative eigenvalue and satisfies the Strong Arnold Property. The CdV number of G is the maximum nullity of a CdV matrix of G. A matrix for which the maximum is obtained is called an optimal CdV matrix. The CdV number has the magical property that G is planar if and only if its CdV number is less than4. A lower bound for the CdV number is the clique number minus 1. For chordal graphs, the clique number is an upper bound. Split graphs are chordal graphs. For split graphs we show when any of the two values is the value of the CdV number and construct a CdV matrix which is optimal when the CdV number is equal to the clique number minus 1. The talk is based on a paper with Felix Goldberg.