Results 11 to 20 of about 6,063,894 (295)
The Bipartite Zero Forcing Set for a Full Sign Pattern Matrix [PDF]
Mathematics, 2020 For an m × n sign pattern P, we define a signed bipartite graph B ( U , V ) with one set of vertices U = { 1 , 2 , … , m } based on rows of P and the other set of vertices V = { 1 ′ , 2 ′ , … ,
Gu-Fang Mou +2 more
doaj +3 more sources
Zero forcing irredundant sets [PDF]
Australas. J Comb.Irredundance has been studied in the context of dominating sets, via the concept of private neighbor. Here irredundance of zero forcing sets is introduced via the concept of a private fort and the upper and lower zero forcing irrdedundance numbers $\mbox{ZIR}(G)$ and $\mbox{zir}(G)$ are defined.
Bryan Curtis +2 more
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Power Edge Set and Zero Forcing Set Remain Difficult in Cubic Graphs
, 2019 This paper presents new complexity and non-approximation results concerning two color propagation problems, namely Power Edge Set and Zero Forcing Set. We focus on cubic graphs, exploiting their structural properties to improve and refine previous results.
Cazals, Pierre +4 more
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Using variants of zero forcing to bound the inertia set of a graph [PDF]
The Electronic Journal of Linear Algebra, 2015 Zero forcing is a combinatorial game played on a graph with a goal of changing the color of every vertex at minimal cost. This leads to a parameter known as the zero forcing number that can be used to give an upper bound for the maximum nullity of a matrix associated with the graph. A variation on the zero forcing game is introduced that can be used to
Steve Butler, Jason Grout, H. Hall
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Exploring the influence of graph operations on zero forcing sets [PDF]
Discrete MathematicsZero forcing in graphs is a coloring process where a colored vertex can force its unique uncolored neighbor to be colored. A zero forcing set is a set of initially colored vertices capable of eventually coloring all vertices of the graph. In this paper, we focus on the numbers $z(G; i)$, which is the number of zero forcing sets of size $i$ of the graph
Krishna Menon, Anurag Singh 0003
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Proper colorings from positive semidefinite zero forcing sets
Journal of Discrete Mathematical Sciences and Cryptography, 2016 AbstractWe present a method to construct a proper coloring of a graph from a positive semidefinite zero forcing set.
Mitchell, Lon, Lon Mitchell
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Variations of zero forcing and power domination [PDF]
, 2021 Zero forcing is a propagation process on a graph that turns white vertices into blue vertices. In this process, an initial set of vertices in a graph $G$ are chosen to be blue and all others are colored white, then a color-change rule is iteratively ...
Alameda, Joseph, Joseph Alameda
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Zero-Forcing Processes on Proper Interval Graphs and Twisted Hypercubes [PDF]
, 2023 Zero forcing is a graph infection process where a colour change rule is applied iteratively to a graph and an initial set of vertices, S. If S results in the entire graph becoming infected, we call this set a zero forcing set.
Collier, Peter
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Total forcing sets and zero forcing sets in trees
Discussiones Mathematicae Graph Theory, 2020 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Randy Davila, Michael A. Henning
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, 2022 In this paper, we study minimal (with respect to inclusion) zero forcing sets. We first investigate when a graph can have polynomially or exponentially many distinct minimal zero forcing sets. We also study the maximum size of a minimal zero forcing set $\overline{\operatorname{Z}}(G)$, and relate it to the zero forcing number $\operatorname{Z}(G ...
Brimkov, Boris, Carlson, Joshua
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