Results 11 to 20 of about 26,712 (151)
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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A Short Proof for a Lower Bound on the Zero Forcing Number
Discussiones Mathematicae Graph Theory, 2020 We provide a short proof of a conjecture of Davila and Kenter concerning a lower bound on the zero forcing number Z(G) of a graph G. More specifically, we show that Z(G) ≥ (g − 2)(δ − 2) + 2 for every graph G of girth g at least 3 and minimum degree δ at
Fürst Maximilian, Rautenbach Dieter
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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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On the Zero Forcing Number and Spectral Radius of Graphs [PDF]
The Electronic Journal of Combinatorics, 2022 In this paper, we determine the graphs (respectively, trees) with maximum spectral radius among all graphs (respectively, trees) with zero forcing number at most $k$. As an application, we give a sharp lower bound for the zero forcing number of graphs involving the spectral radius.
Wenqian Zhang 0002 +3 more
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Spectral bounds for the zero forcing number of a graph
Discussiones Mathematicae Graph TheorySummary: Let \(Z(G)\) be the zero forcing number of a simple connected graph \(G\). In this paper, we study the relationship between the zero forcing number of a graph and its (normalized) Laplacian eigenvalues. We provide the upper and lower bounds on \(Z(G)\) in terms of its (normalized) Laplacian eigenvalues, respectively.
Hongzhang Chen, Jianxi Li, Shou-Jun Xu
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On zero forcing number of graphs and their complements [PDF]
Discrete Mathematics, Algorithms and Applications, 2015 The zero forcing number, Z(G), of a graph G is the minimum cardinality of a set S of black vertices (whereas vertices in V(G)\S are colored white) such that V(G) is turned black after finitely many applications of "the color-change rule": a white vertex is converted to a black vertex if it is the only white neighbor of a black vertex.
Linda Eroh, Cong X. Kang, Eunjeong Yi
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A lower bound on the zero forcing number [PDF]
Discrete Applied Mathematics, 2018 In this note, we study a dynamic vertex coloring for a graph $G$. In particular, one starts with a certain set of vertices black, and all other vertices white. Then, at each time step, a black vertex with exactly one white neighbor forces its white neighbor to become black.
Randy Davila +2 more
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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 +4 more
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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 +2 more
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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
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