dc.contributor.advisor Hicks, Illya V Davila, Randy R 2016-01-07T17:28:35Z 2016-01-07T17:28:35Z 2015-05 2015-04-16 May 2015 Davila, Randy R. "Bounding the Forcing Number of a Graph." (2015) Master’s Thesis, Rice University. https://hdl.handle.net/1911/87761. https://hdl.handle.net/1911/87761 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. application/pdf eng Zero Forcing Numberk-Forcing Number Bounding the Forcing Number of a Graph Thesis Tapia, Richard A Zhang, Yin 2016-01-07T17:28:36Z Text Computational and Applied Mathematics Engineering Rice University Masters Master of Arts
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