Positive semidefinite maximum nullity and zero forcing number
Positive semidefinite maximum nullity and zero forcing number
复制标题
正半定最大无效性和迫零数
DOI：
10.13001/1081-3810.1559
复制
发表时间：
2012
影响因子：
0.7
通讯作者：
Travis Peters
中科院分区：
文献类型：
--
作者：
Travis Peters
零强迫数Z(G)用于研究由简单无向图G描述的对称矩阵族的最小秩/最大零性。正半无穷零强迫数是（标准）零强迫数的一个变体，它使用相同的定义，只是不同的变色规则。计算了各种图族的正半定最大零值和零强迫数。此外，通过证明存在一个普遍最优的正半定矩阵，建立了超立方体最小秩的场无关性。
The zero forcing number Z(G) is used to study the minimum rank/maximum nullity of the family of symmetric matrices described by a simple, undirected graph G. The positive semidef- inite zero forcing number is a variant of the (standard) zero forcing number, which uses the same definition except with a different color-change rule. The positive semidefinite maximum nullity and zero forcing number for a variety of graph families are computed. In addition, field independence of the minimum rank of the hypercube is established, by showing there is a positive semidefinite matrix that is universally optimal.