Zobrazeno 1 - 10
of 27
pro vyhledávání: '"Minimum rank of a graph"'
Autor:
Jephian C.-H. Lin, Carlos A. Alfaro
Publikováno v:
Applied Mathematics and Computation. 358:305-313
There are profound relations between the zero forcing number and minimum rank of a graph. We study the relation of both parameters with a third one, the algebraic co-rank, which is defined as the largest i such that the ith critical ideal is trivial.
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::854a8f83ce4a9029e1c0238bbb600061
https://doi.org/10.1016/j.amc.2019.04.043
https://doi.org/10.1016/j.amc.2019.04.043
Publikováno v:
Journal of Combinatorial Optimization. 37:970-988
Zero forcing is a graph propagation process introduced in quantum physics and theoretical computer science, and closely related to the minimum rank problem. The minimum rank of a graph is the smallest possible rank over all matrices described by a gi
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::caa741126c6af89752b44798a645e423
https://doi.org/10.1007/s10878-018-0335-1
https://doi.org/10.1007/s10878-018-0335-1
Autor:
Franklin H. J. Kenter
Publikováno v:
Operations Research Letters. 44:255-259
The minimum rank problem asks to find the minimum rank over all matrices with a given pattern associated with a graph. This problem is NP-hard, and there is no known approximation method. Further, this problem has no straightforward convex relaxation
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::ba8ceae400e327be0cbe758600b50c0b
https://doi.org/10.1016/j.orl.2016.02.001
https://doi.org/10.1016/j.orl.2016.02.001
Publikováno v:
Linear Algebra and its Applications. 438:3913-3948
Let F be a field, let G be an undirected graph on n vertices, and let SF(G) be the class of all F-valued symmetric n×n matrices whose nonzero off-diagonal entries occur in exactly the positions corresponding to the edges of G. For each graph G, ther
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::18298cb34745fb27bd266eada4a0579b
https://doi.org/10.1016/j.laa.2011.12.036
https://doi.org/10.1016/j.laa.2011.12.036
Autor:
Andrew Zimmer
Publikováno v:
Linear Algebra and its Applications. 438:1095-1112
The real positive semidefinite minimum rank of a graph is the minimum rank among all real positive semidefinite matrices that are naturally associated via their zero-nonzero pattern to the given graph. In this paper, we use orthogonal vertex removal
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::32e39971a2d811c89e387631ff3f1f69
https://doi.org/10.1016/j.laa.2012.09.001
https://doi.org/10.1016/j.laa.2012.09.001
Autor:
Bahman Ahmadi, Shaun M. Fallat, Shahla Nasserasr, Fatemeh Alinaghipour, Karen Meagher, Yi-Zheng Fan
Publikováno v:
Linear Algebra and its Applications. 437:2064-2076
In this paper we introduce a new parameter for a graph called the {\it minimum universal rank}. This parameter is similar to the minimum rank of a graph. For a graph $G$ the minimum universal rank of $G$ is the minimum rank over all matrices of the f
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::ea16d16515b9587236d6f299c09e25b9
https://doi.org/10.1016/j.laa.2012.05.033
https://doi.org/10.1016/j.laa.2012.05.033
Autor:
Francesco Barioli, Shaun M. Fallat, H. Tracy Hall, Leslie Hogben, Hein van der Holst, Wayne Barrett
Publikováno v:
Linear Algebra and Its Applications, 436(12), 4373-4391. Elsevier
The minimum rank of a graph has been an interesting and well studied parameter investigated by many researchers over the past decade or so. One of the many unresolved questions on this topic is the so-called graph complement conjecture, which grew ou
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::8b5f7c6e9e88692e95e548ab6d64ecd2
https://doi.org/10.1016/j.laa.2010.12.024
https://doi.org/10.1016/j.laa.2010.12.024
Publikováno v:
Linear Algebra and its Applications. 433(3):585-594
For a simple graph G on n vertices, the minimum rank of G over a field F , written as mr F ( G ) , is defined to be the smallest possible rank among all n × n symmetric matrices over F whose ( i , j ) th entry (for i ≠ j ) is nonzero whenever { i
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::f16e7e8fc7e4ee6d775df5d9923bea5a
Publikováno v:
Linear Algebra and its Applications. 432(1):430-440
The minimum rank of a graph is the smallest possible rank among all real symmetric matrices with the given graph. The minimum semidefinite rank of a graph is the minimum rank among Hermitian positive semidefinite matrices with the given graph. We exp
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::1676228e77cfdf62297b2ffc0cd3d14e
Publikováno v:
Linear Algebra and its Applications. 429(7):1629-1638
For a graph G of order n , the minimum rank of G is defined to be the smallest possible rank over all real symmetric n × n matrices A whose ( i , j ) th entry (for i ≠ j ) is nonzero whenever { i , j } is an edge in G and is zero otherwise. We pro
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::660868861f0f198bcfe35afaacb9a43a