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- W2963157019 abstract "The zero-forcing number, Z(G) is an upper bound for the maximum nullity of all symmetric matrices with a sparsity pattern described by the graph. A simple lower bound is δ ≤ Z(G) where δ is the minimum degree. An improvement of this bound is provided in the case that G has girth of at least 5. In particular, it is shown that 2δ − 2 ≤ Z(G) for graphs with girth of at least 5; this can be further improved when G has a small cut set. Lastly, a conjecture is made regarding a lower bound for Z(G) as a function of the girth, g, and δ; this conjecture is proved in a few cases and numerical evidence is provided." @default.
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- W2963157019 date "2015-07-07" @default.
- W2963157019 modified "2023-10-17" @default.
- W2963157019 title "Bounds for the Zero Forcing Number of Graphs with Large Girth" @default.
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- W2963157019 doi "https://doi.org/10.20429/tag.2015.020201" @default.
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