Results 11 to 20 of about 13,009 (241)
Maximum nullity and zero forcing number of graphs with rank at most 4
Cogent Mathematics & Statistics, 2018 Let G be a simple graph with n vertices. The rank of G is the number of non-zero eigenvalues of its adjacency matrix and denoted by rank(G).
Ebrahim Vatandoost, Katayoun Nozari
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Maximum generic nullity of a graph
Linear Algebra and its Applications, 2009 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Leslie Hogben, Bryan L. Shader
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Zero forcing and maximum nullity for hypergraphs [PDF]
Discrete Applied Mathematics, 2019 The concept of zero forcing is extended from graphs to uniform hypergraphs in analogy with the way zero forcing was defined as an upper bound for the maximum nullity of the family of symmetric matrices whose nonzero pattern of entries is described by a given graph: A family of symmetric hypermatrices is associated with a uniform hypergraph and zeros ...
Leslie Hogben
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Line graphs: Their maximum nullities and zero forcing numbers [PDF]
Czechoslovak Mathematical Journal, 2016 The main aim of this paper is to analyze the maximum nullity and zero forcing number, and their positive counterparts, for general families of line graphs associated with graphs possessing some specific properties. In [\textit{F. Barioli} et al., Linear Algebra Appl. 428, No.
Shaun Fallat, Abolghasem Soltani
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Two-connected signed graphs with maximum nullity at most two [PDF]
Linear Algebra and its Applications, 2020 A signed graph is a pair $(G, )$, where $G=(V,E)$ is a graph (in which parallel edges are permitted, but loops are not) with $V=\{1,\ldots,n\}$ and $ \subseteq E$. The edges in $ $ are called odd and the other edges of $E$ even. By $S(G, )$ we denote the set of all symmetric $n\times n$ matrices $A=[a_{i,j}]$ with $a_{i,j}<0$ if $i$ and $j$ are ...
Marina Arav +3 more
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Techniques for determining equality of the maximum nullity and the zero forcing number of a graph
The Electronic Journal of Linear Algebra, 2021 It is known that the zero forcing number of a graph is an upper bound for the maximum nullity of the graph (see [AIM Minimum Rank - Special Graphs Work Group (F. Barioli, W. Barrett, S. Butler, S. Cioab$\breve{\text{a}}$, D. Cvetkovi$\acute{\text{c}}$, S. Fallat, C. Godsil, W. Haemers, L. Hogben, R. Mikkelson, S. Narayan, O. Pryporova, I.
Derek Young
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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 K. Narayan
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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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On the tree cover number and the positive semidefinite maximum nullity of a graph [PDF]
, 2018 For a simple graph $G=(V,E),$ let $\mathcal{S}_+(G)$ denote the set of real positive semidefinite matrices $A=(a_{ij})$ such that $a_{ij}\neq 0$ if $\{i,j\}\in E$ and $a_{ij}=0$ if $\{i,j\}\notin E$. The maximum positive semidefinite nullity of $G$, denoted $\operatorname{M}_+(G),$ is $\max\{\operatorname{null}(A)|A\in \mathcal{S}_+(G)\}.$ A tree cover
Chassidy Bozeman
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On the maximum positive semi-definite nullity and the cycle matroid of graphs
The Electronic Journal of Linear Algebra, 2009 Let G = (V,E) be a graph with V = {1, 2, ¿ ,n}, in which we allow parallel edges but no loops, and let S+(G) be the set of all positive semi-definite n × n matrices A = [ai,j] with ai,j = 0 if i ¿ j and i and j are non-adjacent, ai,j ¿ 0 if i ¿ j and i and j are connected by exactly one edge, and ai,j e if i = j or i and j are connected by parallel ...
Hein van der Holst
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