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Reconfiguration Graphs of Zero Forcing Sets

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 $
Leslie Hogben, Ruth Haas, Jesse T. Geneson   +2 more
exaly   +5 more sources

Positive Semidefinite Zero Forcing [PDF]

Linear Algebra and Its Applications, 2013
The positive semidefinite zero forcing number Z+(G) of a graph G was introduced in [4]. We establish a variety of properties of Z+(G): Any vertex of G can be in a minimum positive semidefinite zero forcing set (this is not true for standard zero forcing).
Craig Jeremy Erickson, Leslie Hogben, Nathan Wärnberg   +2 more
exaly   +1 more source

All Graphs With a Failed Zero Forcing Number of Two

Symmetry, 2021
Given a graph G, the zero forcing number of G, Z(G), is the smallest cardinality of any set S of vertices on which repeated applications of the forcing rule results in all vertices being in S.
Darren A Narayan
exaly   +2 more sources

Fractional Zero Forcing via Three-Color Forcing Games [PDF]

Discrete Applied Mathematics, 2016
An r-fold analogue of the positive semidefinite zero forcing process that is carried out on the r-blowup of a graph is introduced and used to define the fractional positive semidefinite forcing number.
David E Robérson, Leslie Hogben, Michael Young   +2 more
exaly   +1 more source

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Isomorphisms and Properties of TAR Graphs for Zero Forcing and Other X-set Parameters

Graphs and Combinatorics, 2023
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Novi H. Bong, Joshua Carlson, Bryan Curtis, Ruth Haas, Leslie Hogben   +4 more
openaire   +1 more source

New computational approaches for the power dominating set problem: Set covering and the neighborhoods of zero forcing forts

Networks, 2021
AbstractTo monitor electrical activity throughout the power grid and mitigate outages, sensors known as phasor measurement units can installed. Due to implementation costs, it is desirable to minimize the number of sensors deployed while ensuring that the grid can be effectively monitored.
Logan A. Smith, Illya V. Hicks
openaire   +1 more source

MINIMUM ZERO-FORCING SETS OF VARIOUS GRAPHS: INSIGHTS AND REAL-WORLD APPLICATIONS

ShodhKosh: Journal of Visual and Performing Arts, 2022
Let each vertex of a graph G = (V (G), E(G)) be given one of two colours, say, “black” and “white”. Let Z denote the (initial) set of black vertices of G. The colour-change rule converts the colour of a vertex from white to black if the white vertex is the only white neighbour of a black vertex. Set Z is a zero forcing set of G if all vertices of G are
Susanth P, Sunitha P
openaire   +1 more source

Some Algebraic Hyperstructures Related to Zero Forcing Sets and Forcing Digraphs

Journal of Algebra and Its Applications, 2019
A zero forcing set is a new concept in Graph Theory which was introduced in recent years. In this paper, we investigate the relationship between zero forcing sets and algebraic hyperstructures. To this end, we present some new definitions by considering a zero forcing process on a graph [Formula: see text].
Golmohamadian, M., Zahedi, M. M., Soltankhah, N.   +2 more
exaly   +2 more sources