Results 11 to 20 of about 494 (225)
The Number of P-Vertices of Singular Acyclic Matrices: An Inverse Problem
Discussiones Mathematicae Graph Theory, 2020 Let A be a real symmetric matrix. If after we delete a row and a column of the same index, the nullity increases by one, we call that index a P-vertex of A.
Du Zhibin, da Fonseca Carlos M.
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On the nullity number of graphs
Electronic Journal of Graph Theory and Applications, 2017 The paper discusses bounds on the nullity number of graphs. It is proved in [B. Cheng and B. Liu, On the nullity of graphs. Electron. J. Linear Algebra 16 (2007) 60--67] that $\eta \le n - D$, where $\eta$, n and D denote the nullity number, the order ...
Mustapha Aouchiche, Pierre Hansen
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Linear Algebra and its Applications, 2005 The nullity of a graph is the multiplicity of the eigenvalue zero in its spectrum. Among all \(n\)-vertex trees, the star tree has greatest nullity (equal to \(n-2\)). In this paper it is shown that among all \(n\)-vertex trees whose vertex degrees do not exceed a fixed value \(D\), the greatest nullity is \(n- 2 \lceil (n-1)/D \rceil\).
Fiorini, Stanley +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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Maximum generic nullity of a graph
Linear Algebra and its Applications, 2010 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Hogben, Leslie, Shader, Bryan
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Arquivo Brasileiro de Medicina Veterinária e Zootecnia, 2008 Estimaram-se o valor energético das forrageiras e o consumo de matéria seca por novilhas, em função do ganho de peso, criadas em pastagens de capim-elefante (Pennisetum purpureum Schum. cv. Napier) e capim-mombaça (Panicum maximum, cv.
F.N. Lista +4 more
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Tree Cover Number and Maximum Semidefinite Nullity of Some Graph Classes
The Electronic Journal of Linear Algebra, 2020 Let $G$ be a graph with a vertex set $V$ and an edge set $E$ consisting of unordered pairs of vertices. The tree cover number of $G$, denoted $\tau(G)$, is the minimum number of vertex disjoint simple trees occurring as induced subgraphs of $G$ that cover all the vertices of $G$.
Rachel Domagalski, Sivaram Narayan
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Maximum nullity of Cayley graph
, 2017 One of the most interesting problems on maximum nullity (minimum rank) is to characterize $M(\mathcal{G})$ ($mr(\mathcal{G})$) for a graph $\mathcal{G}$. In this regard, many researchers have been trying to find an upper or lower bound for the maximum nullity. For more results on this topic, see \cite{4}, \cite{2}, \cite{10} and \cite{1}. In this paper,
Vatandoost, Ebrahim +1 more
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A Zero‐Rank, Maximum Nullity Perfect Electromagnetic Wave Absorber
Advanced Optical Materials, 2019 AbstractElectromagnetic wave absorbers formed from a metamaterial layer are demonstrated and near‐perfect absorption is realized across much of the spectrum. Alternatively, an unpatterned low‐loss dielectric layer forms an absorber of coherent light and shows near‐zero reflectance and high absorption.
Jonathan Y. Suen +2 more
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Minimum rank, maximum nullity and zero forcing number for selected graph families [PDF]
Involve, a Journal of Mathematics, 2010 The minimum rank of a simple graph G is dened to be the smallest possible rank over all symmetric real matrices whose ijth entry (for i 6 j) is nonzero whenever fi;jg is an edge in G and is zero otherwise. Maximum nullity is taken over the same set of matrices, and the sum of maximum nullity and minimum rank is the order of the graph.
Almodovar, Edgard +6 more
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