Results 31 to 40 of about 13,009 (241)

Path cover number, maximum nullity, and zero forcing number of oriented graphs and other simple digraphs [PDF]

Involve, a Journal of Mathematics, 2015
∗Department of Mathematics, Statistics, and Computer Science, St. Olaf College, Northfield, MN 55057 (berliner@stolaf.edu), (coxn@stolaf.edu). Research of N. Cox supported by NSF DMS 0750986 †Department of Mathematics, Carleton College, Northfield, MN 55057 (brownc@carleton.edu). Research supported by NSF DMS 0750986.
Adam H. Berliner, C.P. Brown, Joshua Carlson, Nathanael Cox, Leslie Hogben, Jason C. Hu, Katrina Jacobs, Kathryn Manternach, Travis Peters, Nathan Warnberg, Michael E. Young   +10 more
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The maximum nullity of a complete subdivision graph is equal to its zero forcing number

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.
Wayne Barrett, Steve Butler, Minerva Catral, Shaun Fallat, H. Tracy Hall, Leslie Hogben, Michael Young   +6 more
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The Classification of Graphs on $8$ vertices with Coinciding Zero Forcing number and Maximum Nullity [PDF]

We study the minimum rank of a (simple, undirected) graph, which is the minimum rank among all matrices in a space determined by the graph. We determine the exact set of graphs on eight vertices for which the nullity of a minimum rank matrix does not coincide with a bound determined by the zero forcing number of a graph.
Wayne Barrett, Mark Hunnell, John Hutchens, John Sinkovic   +3 more
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Parameters Related to Tree‐Width, Zero Forcing, and Maximum Nullity of a Graph

Journal of Graph Theory, 2012
AbstractTree‐width, and variants that restrict the allowable tree decompositions, play an important role in the study of graph algorithms and have application to computer science. The zero forcing number is used to study the maximum nullity/minimum rank of the family of symmetric matrices described by a graph.
Francesco Barioli, Wayne Barrett, Shaun Fallat, H. Tracy Hall, Leslie Hogben, Bryan L. Shader, P. van den Driessche, Hein van der Holst   +7 more
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Vertex and edge spread of zero forcing number, maximum nullity, and minimum rank of a graph

Linear Algebra and its Applications, 2010
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Christina J. Edholm, Leslie Hogben, My Huynh, Joshua LaGrange, Darren D. Row   +4 more
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Change of nullity of a graph under two operations

Kuwait Journal of Science, 2021
Two adjacent or non-adjacent vertices of a graph G are said to be identified, if they are combined to form one vertex whose neighbor is the union of their neighborhoods (ignoring any loops or multiple edges formed).
Gohdar H. Mohiaddin, Khidir R. Sharaf
doaj   +1 more source

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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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, Tian-Fei Wang, Zhong-Shan Li   +2 more
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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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