On minimum rank and zero forcing sets of a graph

Liang Hao Huang, Gerard J. Chang, Hong Gwa Yeh

研究成果: 雜誌貢獻期刊論文同行評審

40 引文 斯高帕斯(Scopus)

摘要

For a graph G on n vertices and a field F, the minimum rank of G over F, written as mrF (G), is the smallest possible rank over all n × n symmetric matrices over F whose (i, j)th entry (for i ≠ j) is nonzero whenever ij is an edge in G and is zero otherwise. The maximum nullity of G over F is MF (G) = n - mrF (G). The minimum rank problem of a graph G is to determine mrF (G) (or equivalently, MF (G)). This problem has received considerable attention over the years. In [F. Barioli, W. Barrett, S. Butler, S.M. Cioabǎ, D. Cvetković, S.M. Fallat, C. Godsil, W. Haemers, L. Hogben, R. Mikkelson, S. Narayan, O. Pryporova, I. Sciriha, W. So, D. Stevanović, H. van der Holst, K.V. Meulen, A.W. Wehe, AIM Minimum Rank-Special Graphs Work Group, Zero forcing sets and the minimum rank of graphs, Linear Algebra Appl. 428 (2008) 1628-1648], a new graph parameter Z (G), the zero forcing number, was introduced to bound MF (G) from above. The authors posted an attractive question: What is the class of graphs G for which Z (G) = MF (G) for some field F? This paper focuses on exploring the above question.

原文???core.languages.en_GB???
頁(從 - 到)2961-2973
頁數13
期刊Linear Algebra and Its Applications
432
發行號11
DOIs
出版狀態已出版 - 1 6月 2010

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