Results 21 to 30 of about 5,825,526 (293)
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
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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
Zero Forcing Sets and Controllability of Dynamical Systems Defined on Graphs [PDF]
IEEE Transactions on Automatic Control, 2014 In this paper, controllability of systems defined on graphs is discussed. We consider the problem of controllability of the network for a family of matrices carrying the structure of an underlying directed graph. A one-to-one correspondence between the set of leaders rendering the network controllable and zero forcing sets is established. To illustrate
Nima Monshizadeh +2 more
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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
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
Zero and total forcing dense graphs [PDF]
, 2023 If $S$ is a set of colored vertices in a simple graph $G$, then one may allow a colored vertex with exactly one non-colored neighbor to force its non-colored neighbor to become colored.
Randy Davila +5 more
core +1 more source
Spreading in claw-free cubic graphs [PDF]
Opuscula MathematicaLet \(p \in \mathbb{N}\) and \(q \in \mathbb{N} \cup \lbrace \infty \rbrace\). We study a dynamic coloring of the vertices of a graph \(G\) that starts with an initial subset \(S\) of blue vertices, with all remaining vertices colored white.
Boštjan Brešar +2 more
doaj +1 more source
ZERO FORCING NUMBER AND MAXIMUM NULLITY OF GENERAL POWER GRAPHS [PDF]
Journal of Algebraic SystemsLet 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
0034 | Zero Forcing Number in Neutrosophic Graphs
, 2022 In this book, some notions are introduced about “Zero Forcing Number in Neutrosophic Graphs.” Three chapters are devised as “Common Notions”, “Modified Notions” and “Extended Notions”. Three manuscripts are cited as the references of these chapters which
Henry Garrett
core +1 more source
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 +12 more
core +1 more source