Abstract
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.
Original language | English |
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Pages (from-to) | 1628-1648 |
Journal | Linear Algebra and Its Applications |
Volume | 428 |
Issue number | 7 |
DOIs | |
Publication status | Published - 2008 |