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Expected propagation time for probabilistic zero forcing [PDF]

, 2022
Zero forcing is a coloring process on a graph that was introduced more than fifteen years ago in several different applications. The goal is to color all the vertices blue by repeated use of a (deterministic) color change rule. Probabilistic zero forcing
Hogben, Leslie, Geneson, Jesse
core  

Line graphs: their maximum nullities and zero forcing numbers [PDF]

, 2008
summary:The maximum nullity over a collection of matrices associated with a graph has been attracting the attention of numerous researchers for at least three decades.
Fallat, Shaun, Wang, Wendy, Johnson, Charles, Harris, Benjamin, Lay, Margaret, Soltani, Abolghasem, Mitchell, Lon, Narayan, Sivaram, Steinmetz, Kelly, Sutton, Brian, Hackney, Philip, Booth, Mathew, Pascoe, Amanda   +12 more
core   +1 more source

Open global shadow graph and it’s zero forcing number

, 2023
Zero forcing number of a graph is the minimum cardinality of the zero forcing set. A zero forcing set is a set of black vertices of minimum cardinality that can colour the entire graph black using the color change rule: each vertex of G is coloured ...
Malur, Raksha, Dominic, Charles
core   +1 more source

The Bipartite Zero Forcing Set for a Full Sign Pattern Matrix

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, Tian-Fei Wang, Zhong-Shan Li   +2 more
doaj   +1 more source

A Periodically Rotating Distributed Forcing of Flow over a Sphere for Drag Reduction

Mathematics, 2023
In the present study, we propose a periodically rotating distributed forcing for turbulent flow over a sphere for its drag reduction. The blowing/suction forcing is applied on a finite slot of the sphere surface near the flow separation, and unsteady ...
Donggun Son, Jungil Lee
doaj   +1 more source

The Forcing Domination Number of Hamiltonian Cubic Graphs [PDF]

, 2009
The authors presented a sequence of Hamiltonian cubic graphs whose domination numbers are sharp and in this paper we study forcing domination number for those ...
H. Abdollahzadeh Ahangar, H.Abdollahzadeh Ahangar, Abdollahzadeh Ahangar, H., Pushpalatha L.   +3 more
core   +1 more source

Maximum nullity and zero forcing of circulant graphs

Special Matrices, 2020
The zero forcing number of a graph has been applied to communication complexity, electrical power grid monitoring, and some inverse eigenvalue problems.
Duong Linh, Kroschel Brenda K., Riddell Michael, Vander Meulen Kevin N., Van Tuyl Adam   +4 more
doaj   +1 more source

Brushing Number and Zero-Forcing Number of Graphs and Their Line Graphs [PDF]

Graphs and Combinatorics, 2018
15 ...
Aras Erzurumluoglu, Karen Meagher, David A. Pike   +2 more
openaire   +4 more sources

ZERO FORCING NUMBER AND MAXIMUM NULLITY OF GENERAL POWER GRAPHS [PDF]

Journal of Algebraic Systems
Let Γ = (V,E) be a simple and undirected graph. General power graph of Γ, shown by Pg(Γ), is a graph with the vertex set P(V (Γ))\ϕ. Also two distinct vertices of B and C are adjacent if and only if every b ∈ B is adjacent to every c ∈ C \{b} in Γ.
Fateme Kheiridosst, Ebrahim Vatandoost
doaj   +1 more source

The failed zero forcing number of a graph [PDF]

Involve, a Journal of Mathematics, 2015
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 color change rule results in all vertices joining S. The color change rule is: if a vertex v is in S, and exactly one neighbor u of v is not in S, then u joins S in the next iteration.
Fetcie, Katherine, Jacob, Bonnie, Saavedra, Daniel   +2 more
openaire   +2 more sources