Zero forcing sets and minimum rank of graphs
Zero forcing sets and minimum rank of graphs
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DOI：
10.1016/j.laa.2007.10.009
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发表时间：
2008
影响因子：
6.3
通讯作者：
W. Haemers
中科院分区：
文献类型：
--
作者：
W. Haemers
简单图G的最小秩被定义为所有对称真实的矩阵的最小可能秩，当{i，j}是G的边时，矩阵的第ij个元素（对于i ∈ j）不为零，否则为零.本文引入了一个新的图参数Z（G），它是迫零顶点集的最小尺寸，并利用它来确定许多图族的最小秩，从而可以计算最小秩。
The minimum rank of a simple graph G is defined to be the smallest possible rank over all symmetric real matrices whose ijth entry (for i≠j) is nonzero whenever {i,j} is an edge in G and is zero otherwise. This paper introduces a new graph parameter, Z(G), that is the minimum size of a zero forcing set of vertices and uses it to bound the minimum rank for numerous families of graphs, often enabling computation of the minimum rank.