Results 11 to 20 of about 409,696 (282)
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 $
Jesse Geneson, Ruth Haas, Leslie Hogben
openaire +4 more sources
Robust Strong Structural Controllability of Complex Power Systems
Frontiers in Energy Research, 2022 Ensuring the control of power systems is crucial for their safe operation. This paper analyses the robust controllability of complex power systems from the structural sighta structural point of view.
Yunhe Sun +3 more
doaj +1 more source
, 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
openaire +3 more sources
Total forcing sets and zero forcing sets in trees
Discussiones Mathematicae Graph Theory, 2020 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Davila Randy, Henning Michael A.
openaire +3 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 +1 more source
Equalization-Based Beamforming for Secure Multicasting in Multicast Wiretap Channels
IEEE Access, 2021 In this paper, a beamforming scheme is proposed to maximize a secrecy multicast rate (SMR) in the multicast wiretap channel, in which the multiple unauthorized users overhear the multicast messages.
Duckdong Hwang +4 more
doaj +1 more source
Topological and Graph-coloring Conditions on the Parameter-independent Stability of Second-order Networked Systems [PDF]
, 2017 In this paper, we study parameter-independent stability in qualitatively heterogeneous passive networked systems containing damped and undamped nodes.
Bürger, Mathias +3 more
core +5 more sources
Metric Dimension on Sparse Graphs and its Applications to Zero Forcing Sets [PDF]
SSRN Electronic Journal, 2021 The metric dimension dim(G) of a graph $G$ is the minimum cardinality of a subset $S$ of vertices of $G$ such that each vertex of $G$ is uniquely determined by its distances to $S$. It is well-known that the metric dimension of a graph can be drastically increased by the modification of a single edge.
Bousquet, Nicolas +3 more
openaire +2 more sources
Fractional Zero Forcing via Three-color Forcing Games [PDF]
, 2015 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. Properties of the graph blowup when colored with
Hogben, Leslie +4 more
core +4 more sources
Bounds for the Zero Forcing Number of Graphs with Large Girth
Theory and Applications of Graphs, 2015 The zero-forcing number, Z(G) is an upper bound for the maximum nullity of all symmetric matrices with a sparsity pattern described by the graph. A simple lower bound is δ ≤ Z(G) where δ is the minimum degree.
Randy Davila, Franklin Kenter
doaj +1 more source