Results 11 to 20 of about 9,977,087 (284)
Spectral bounds for the zero forcing number of a graph [PDF]
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
doaj +3 more sources
Failed Zero-Forcing Number in Neutrosophic Graphs
, 2022 New setting is introduced to study failed zero-forcing number and failed zero-forcing neutrosophic-number. Leaf-like is a key term to have these notions. Forcing a vertex to change its color is a type of approach to force that vertex to be zero-like.
Henry Garrett
core +7 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 +6 more sources
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
doaj +5 more sources
Zero Forcing Number in Neutrosophic Graphs
, 2022 New setting is introduced to study zero forcing number and zero forcing neutrosophic-number. Leaf-like is a key term to have these notions. Let NTG : (V,E,σ,μ) be a neutrosophic graph. Then zero forcing number Z(NTG) for a neutrosophic graph NTG : (V,E,σ,
Henry Garrett
openaire +2 more sources
The zero forcing number of graph powers
The $k$-th power of a simple graph $G$, denoted $G^k$, is the graph with vertex set $V(G)$ where two vertices are adjacent if they are within distance $k$ in $G$. We investigate the zero forcing number of graph powers. Powers of graphs are much denser and generally not encompassed by existing results on zero forcing of graphs, hence their study ...
Aida Abiad Monge +3 more
openaire +3 more sources
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
openaire +1 more source
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
openaire +4 more sources
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
openaire +4 more sources
Zero-Forcing Processes on Proper Interval Graphs and Twisted Hypercubes [PDF]
, 2023 Zero forcing is a graph infection process where a colour change rule is applied iteratively to a graph and an initial set of vertices, S. If S results in the entire graph becoming infected, we call this set a zero forcing set.
Collier, Peter
core +2 more sources