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    The maximum nullity of a complete edge subdivision graph is equal to it zero forcing number

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    Date
    2014-06
    Author
    Barrett, Wayne
    Butler, Steve
    Catral, Minnie
    Hall, Tracy
    Fallat, Shaun
    Hogben, Leslie
    Young, Michael
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    URI
    http://hdl.handle.net/10294/5682
    Abstract
    Barrett et al. asked in [W. Barrett et al. Minimum rank of edge subdivisions of graphs. Electronic Journal of Linear Algebra, 18:530–563, 2009.], whether the maximum nullity is equal to the zero forcing number for all complete subdivision graphs. We prove that this equality holds. Furthermore, we compute the value of M(F, °G) = Z(°G) by introducing the bridge tree of a connected graph. Since this equality is valid for all fields, °G has field independent minimum rank, and we also show that °G has a universally optimal matrix.
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    Contact Us | Send Feedback | Archer Library | University of Regina