Zero forcing sets and the minimum rank of graphs

H. Holst, van der, F. Barioli, W. Barrett, S. Butler, S.M. Cioaba, D.M. Cvetkovic, S.M. Fallat, C.D. Godsil, W.H. Haemers, L. Hogben, R. Mikkelson, S. Narayan, O. Pryporova, I. Sciriha, W. So, D. Stevanovic, K.N. Vander Meulen, A. Wangsness Wehe

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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 languageEnglish
Pages (from-to)1628-1648
JournalLinear Algebra and Its Applications
Volume428
Issue number7
DOIs
Publication statusPublished - 2008

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