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    Bounding the Forcing Number of a Graph

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    Author
    Davila, Randy R
    Date
    2015-04-16
    Advisor
    Hicks, Illya V
    Degree
    Master of Arts
    Abstract
    The forcing number, denoted F(G), is an upper bound for the maximum nullity of all symmetric matrices with a sparsity pattern described by the simple graph G. Simple lower and upper bounds are δ ≤ F(G) where δ is the minimum degree and F (G) ≤ n − 1 where n is the order of the graph. This thesis provides improvements on the minimum degree lower bound in the case that G has girth of at least 5. In particular, it is shown that 2δ − 2 ≤ F (G) for graphs with girth of at least 5; this can be further improved when G has a small cut set. Further, this thesis also conjectures a lower bound on F(G) as a function of the girth, g, and δ.
    Keyword
    Zero Forcing Number; k-Forcing Number
    Citation
    Davila, Randy R. "Bounding the Forcing Number of a Graph." (2015) Master’s Thesis, Rice University. https://hdl.handle.net/1911/87761.
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    Managed by the Digital Scholarship Services at Fondren Library, Rice University
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