Results 1 to 10 of about 419,100 (266)
Zero forcing number, constrained matchings and strong structural controllability
Linear Algebra and its Applications, 2015 The zero forcing number is a graph invariant introduced to study the minimum rank of the graph. In 2008, Aazami proved the NP-hardness of computing the zero forcing number of a simple undirected graph.
Delvenne, Jean-Charles, Trefois, Maguy
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Dynamic approach to k-forcing [PDF]
Theory and Applications of Graphs, 2015 The k-forcing number of a graph is a generalization of the zero forcing number. In this note, we give a greedy algorithm to approximate the k-forcing number of a graph. Using this dynamic approach, we give corollaries which improve upon two theorems from
Yair Caro, Ryan Pepper
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On the zero forcing number of generalized Sierpinski graphs [PDF]
Transactions on Combinatorics, 2019 In this article we study the Zero forcing number of Generalized Sierpi\'{n}ski graphs $S(G,t)$. More precisely, we obtain a general lower bound on the Zero forcing number of $S(G,t)$ and we show that this bound is tight.
Ebrahim Vatandoost +2 more
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Minimum rank and zero forcing number for butterfly networks [PDF]
Journal of Combinatorial Optimization, 2018 The minimum rank of a simple graph $G$ is the smallest possible rank over all symmetric real matrices $A$ whose nonzero off-diagonal entries correspond to the edges of $G$.
Ferrero, Daniela +4 more
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On the Relationships between Zero Forcing Numbers and Certain Graph Coverings
Special Matrices, 2014 The zero forcing number and the positive zero forcing number of a graph are two graph parameters that arise from two types of graph colourings. The zero forcing number is an upper bound on the minimum number of induced paths in the graph that cover all ...
Taklimi Fatemeh Alinaghipour +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
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Failed Zero Forcing Numbers of Trees and Circulant Graphs
Theory and Applications of GraphsGiven 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 (described below) results in all vertices being in $S$.
Luis Gomez +4 more
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Properties of SuperHyperGraph and Neutrosophic SuperHyperGraph [PDF]
Neutrosophic Sets and Systems, 2022 New setting is introduced to study dominating, resolving, coloring, Eulerian(Hamiltonian) neutrosophic path, n-Eulerian(Hamiltonian) neutrosophic path, zero forcing number, zero forcing neutrosophicnumber, independent number, independent neutrosophic ...
Henry Garrett
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Connected zero forcing sets and connected propagation time of graphs [PDF]
Transactions on Combinatorics, 2020 The zero forcing number $Z(G)$ of a graph $G$ is the minimum cardinality of a set $S$ with colored (black) vertices which forces the set $V(G)$ to be colored (black) after some times.
Maryam Khosravi +2 more
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Signed zero forcing number and controllability for a networks system with a directed hypercube [PDF]
MATEC Web of Conferences, 2022 The controllability for complex network system is to find the minimum number of leaders for the network system to achieve effective control of the global networks.
Mou Gufang, Zhang Qiuyan
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