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Reconfiguration graphs of zero forcing sets [PDF]
Discrete Applied Mathematics, 2023 This paper begins the study of reconfiguration of zero forcing sets, and more specifically, the zero forcing graph. Given a base graph $G$, its zero forcing graph, $\mathscr{Z}(G)$, is the graph whose vertices are the minimum zero forcing sets of $G$ with an edge between vertices $B$ and $B'$ of $\mathscr{Z}(G)$ if and only if $B$ can be obtained from $
Jesse Geneson +2 more
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Total Forcing Sets and Zero Forcing Sets in Trees
Discussiones Mathematicae Graph Theory, 2020 A dynamic coloring of the vertices of a graph G starts with an initial subset S of colored vertices, with all remaining vertices being non-colored. At each discrete time interval, a colored vertex with exactly one non-colored neighbor forces this non ...
Davila Randy, Henning Michael A.
doaj +3 more sources
Logic circuits from zero forcing. [PDF]
Nat Comput, 2015 5 pages, 10 EPS ...
Burgarth D +4 more
europepmc +7 more sources
Characterization of All Graphs with a Failed Skew Zero Forcing Number of 1
Mathematics, 2022 Given a graph G, the zero forcing number of G, Z(G), is the minimum cardinality of any set S of vertices of which repeated applications of the forcing rule results in all vertices being in S.
Aidan Johnson +2 more
doaj +3 more sources
The Zero Forcing Number of Graphs [PDF]
SIAM Journal on Discrete Mathematics, 2019 A subset S of initially infected vertices of a graph G is called zero forcing if we can infect the entire graph by iteratively applying the following process. At each step, any infected vertex which has a unique uninfected neighbor, infects this neighbor. The zero forcing number of G is the minimum cardinality of a zero forcing set in G.
Thomas Kalinowski +2 more
exaly +4 more sources
Zero and total forcing dense graphs
Discussiones Mathematicae Graph Theory, 2023 Summary: If \(S\) is a set of colored vertices in a simple graph \(G\), then one may allow a colored vertex with exactly one non-colored neighbor to force its non-colored neighbor to become colored. If by iteratively applying this color change rule, all of the vertices in \(G\) become colored, then \(S\) is a zero forcing set of \(G\).
Randy Davila +2 more
doaj +3 more sources
The zero forcing polynomial of a graph
Discrete Applied Mathematics, 2019 23 ...
Boris Brimkov +2 more
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Zero forcing and maximum nullity for hypergraphs [PDF]
Discrete Applied Mathematics, 2020 The concept of zero forcing is extended from graphs to uniform hypergraphs in analogy with the way zero forcing was defined as an upper bound for the maximum nullity of the family of symmetric matrices whose nonzero pattern of entries is described by a given graph: A family of symmetric hypermatrices is associated with a uniform hypergraph and zeros ...
Leslie Hogben
exaly +4 more sources
Propagation time for zero forcing on a graph
Discrete Applied Mathematics, 2012 Poster Presentation Presented at USTARS ...
Leslie Hogben, Michael Young
exaly +6 more sources
Complexity and computation of connected zero forcing
Discrete Applied Mathematics, 2017 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Boris Brimkov, Illya V Hicks
exaly +3 more sources