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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 Erickson, Leslie Hogben, Nathan Wärnberg   +2 more
exaly   +1 more source

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 Robérson, Leslie Hogben, Michael Young   +2 more
exaly   +1 more source

The Zero Forcing Number of Graphs

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.
Thomas Kalinowski, Benny Sudakov, Nina Kamcev   +2 more
exaly   +2 more sources

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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

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.
Karla Rubi, Luis Gomez, Darren A. Narayan, Jorden Terrazas   +3 more
exaly   +2 more sources

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

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
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

Null Space Strong Structural Controllability via Skew Zero Forcing Sets

2018 European Control Conference (ECC), 2018
In this paper, we examine strong structural controllability of a particular subspace of linear time-invariant networks, namely, the null space of the parameterized family of system matrices. In this direction, we establish a one-to-one correspondence between the set of input nodes for null space controllability and the notion of skew zero forcing sets.
Shima Sadat Mousavi, Airlie Chapman, Mohammad Haeri, Mehran Mesbahi   +3 more
openaire   +1 more source

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.
openaire   +2 more sources