Results 21 to 30 of about 2,050,476 (233)
Three-connected graphs whose maximum nullity is at most three [PDF]
Linear Algebra and its Applications, 2008 Let \(G=(V,E)\) be a graph with \(V=\{1,2,\dots,n\}\). Define \(\mathcal S(G)\) as the set of all \(n\times n\) real-valued symmetric matrices \(A=[a_{i,j}]\) with \(a_{i,j}\neq 0\), \(i\neq j\), if and only if \(ij\in E\). The maximum nullity of \(G\), denoted by \(M(G)\), is the largest possible nullity of any matrix \(A\in\mathcal S(G)\).
Holst, van der, H., van der Holst, Hein
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Note on positive semidefinite maximum nullity and positive semidefinite zero forcing number of partial 2-trees [PDF]
The Electronic Journal of Linear Algebra, 2012 The maximum positive semidefinite nullity of a multigraph G is the largest possible nullity over all real positive semidefinite matrices whose (i,j)th entry (for i 6 j) is zero if i and j are not adjacent in G, is nonzero if fi,jg is a single edge, and is any real number if fi,jg is a multiple edge.
Ekstrand, Jason +4 more
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Zero forcing number, maximum nullity, and path cover number of subdivided graphs [PDF]
The Electronic Journal of Linear Algebra, 2012 The zero forcing number, maximum nullity and path cover number of a (simple, undirected) graph are parameters that are important in the study of minimum rank problems. We investigate the effects on these graph parameters when an edge is subdivided to obtain a so-called edge subdivision graph. An open question raised by Barrett et al. is answered in the
Catral, Minerva +6 more
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On the maximum positive semi-definite nullity and the cycle matroid of graphs [PDF]
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 ...
Holst, van der, H.
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The stable maximum nullity of digraphs and $1$-DAGs
Given a digraph $D=(V,A)$ with vertex-set $V=\{1,\ldots,n\}$ and arc-set $A$, we denote by $Q(D)$ the set of all real $n\times n$ matrices $B=[b_{u,w}]$ with $b_{u,u}\not=0$ for all $u\in V$, $b_{u,w} \not= 0$ if $u\not=w$ and there is an arc from $u$ to $w$, and $b_{u,w}=0$ if $u\not=w$ and there is no arc from $u$ to $w$.
Arav, Marina, van der Holst, Hein
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The maximum nullity of a complete subdivision graph is equal to its zero forcing number [PDF]
The Electronic Journal of Linear Algebra, 2014 Barrett et al. asked in [W. Barrett et al. Minimum rank of edge subdivisions of graphs. Electronic Journal of Linear Algebra, 18:530–563, 2009.], whether the maximum nullity is equal to the zero forcing number for all complete subdivision graphs. We prove that this equality holds.
Barrett, Wayne +6 more
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AUTOMATED UAV LIDAR STRIP ALIGNMENT IN FORESTED AREAS USING DENSITY-BASED CANOPY CLUSTERING [PDF]
ISPRS Annals of the Photogrammetry, Remote Sensing and Spatial Information Sciences, 2020 Recently, LiDAR point cloud data acquired by Unmanned Aerial Vehicles (UAVs) are used in many scientific disciplines and like the former photogrammetric techniques these data are usually collected in overlapping strips. Generation of comprehensive models
R. Fekry, W. Yao, L. Cao
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Two-connected signed graphs with maximum nullity at most two [PDF]
Linear Algebra and its Applications, 2021 A signed graph is a pair $(G,Σ)$, where $G=(V,E)$ is a graph (in which parallel edges are permitted, but loops are not) with $V=\{1,\ldots,n\}$ and $Σ\subseteq E$. The edges in $Σ$ are called odd and the other edges of $E$ even. By $S(G,Σ)$ 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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The maximum nullity of a complete edge subdivision graph is equal to it zero forcing number
, 2014 Barrett et al. asked in [W. Barrett et al. Minimum rank of edge subdivisions of graphs. Electronic Journal of Linear Algebra, 18:530–563, 2009.], whether the maximum nullity is equal to the zero forcing number for all complete subdivision graphs. We prove that this equality holds. Furthermore, we compute the value of M(F, °G) = Z(°G) by introducing the
Barrett, Wayne +6 more
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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.
Fallat, Shaun, Soltani, Abolghasem
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