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1Academic Journal
المؤلفون: Fallat, Shaun, Soltani, Abolghasem
مصطلحات موضوعية: keyword:maximum nullity, keyword:zero forcing number, keyword:positive zero forcing number, keyword:line graphs, keyword:matrix, keyword:tree, keyword:positive semidefinite matrix, keyword:unicyclic graph, msc:05C50, msc:15A03, msc:15A18
وصف الملف: application/pdf
Relation: mr:MR3556865; zbl:Zbl 06644031; reference:[1] Group, AIM Minimum Rank -- Special Graphs Work: Zero forcing sets and the minimum rank of graphs.Linear Algebra Appl. 428 (2008), 1628-1648. MR 2388646; reference:[2] Alinaghipour, F.: Zero Forcing Set for Graphs.PhD Dissertation, University of Regina (2013). MR 4272166; reference:[3] Barioli, F., Barrett, W., Fallat, S., Hall, H. T., Hogben, L., Shader, B., Driessche, P. van den, Holst, H. van der: Zero forcing parameters and minimum rank problems.Linear Algebra Appl. 433 (2010), 401-411. MR 2645093; reference:[4] Barioli, F., Fallat, S., Hogben, L.: On the difference between the maximum multiplicity and path cover number for tree-like graphs.Linear Algebra Appl. 409 (2005), 13-31. Zbl 1072.05037, MR 2169544; reference:[5] M. Booth, P. Hackney, B. Harris, C. R. Johnson, M. Lay, L. H. Mitchell, S. K. Narayan, A. Pascoe, K. Steinmetz, B. D. Sutton, W. Wang: On the minimum rank among positive semidefinite matrices with a given graph.SIAM J. Matrix Anal. Appl. 30 (2008), 731-740. MR 2421468, 10.1137/050629793; reference:[6] Edholm, C. J., Hogben, L., Huynh, M., LaGrange, J., Row, D. D.: Vertex and edge spread of zero forcing number, maximum nullity, and minimum rank of a graph.Linear Algebra Appl. 436 (2012), 4352-4372. Zbl 1241.05076, MR 2917414; reference:[7] J. Ekstrand, C. Erickson, H. T. Hall, D. Hay, L. Hogben, R. Johnson, N. Kingsley, S. Osborne, T. Peters, J. Roat, A. Ross, D. D. Row, N. Warnberg, M. Young: Positive semidefinite zero forcing.Linear Algebra Appl. 439 (2013), 1862-1874. MR 3090441; reference:[8] Ekstrand, J., Erickson, C., Hay, D., Hogben, L., Roat, J.: Note on positive semidefinite maximum nullity and positive semidefinite zero forcing number of partial $2$-trees.Electron. J. Linear Algebra. (electronic only) 23 (2012), 79-87. Zbl 1252.05118, MR 2889573; reference:[9] Eroh, L., Kang, C. X., Yi, E.: A Comparison between the Metric Dimension and Zero Forcing Number of Line Graphs.(2012), 14 pages arXiv:1207.6127v1 [math.CO]. MR 3027310; reference:[10] Fallat, S. M., Hogben, L.: Chapter 46: Minimum rank, maximum nullity, and zero forcing number of graphs.Handbook of Linear Algebra L. Hogben CRC Press, Boca Raton (2014), 46-1-46-36. MR 3141806; reference:[11] Fallat, S., Hogben, L.: The minimum rank of symmetric matrices described by a graph: a survey.Linear Algebra Appl. 426 (2007), 558-582. Zbl 1122.05057, MR 2350678; reference:[12] Nylen, P. M.: Minimum-rank matrices with prescribed graph.Linear Algebra Appl. 248 (1996), 303-316. Zbl 0864.05069, MR 1416462; reference:[13] Owens, K.: Properties of the Zero Forcing Number.Master's Thesis, Brigham Young University (2009).; reference:[14] Peters, T.: Positive semidefinite maximum nullity and zero forcing number.Electron. J. Linear Algebra (electronic only) 23 (2012), 815-830. Zbl 1252.05130, MR 2992396; reference:[15] Row, D. D.: A technique for computing the zero forcing number of a graph with a cut-vertex.Linear Algebra Appl. 436 (2012), 4423-4432. Zbl 1241.05086, MR 2917419; reference:[16] Yu, X.: Cyclomatic numbers of connected induced subgraphs.Discrete Math. 105 (1992), 275-284. Zbl 0783.05065, MR 1180211, 10.1016/0012-365X(92)90150-E
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2Academic Journal
المؤلفون: Zhang, Xiao-Dong, Ding, Chang-Xing
مصطلحات موضوعية: keyword:Oppenheim's inequality, keyword:Schur's inequality, keyword:positive semidefinite matrix, keyword:Hadamard product, msc:15A45, msc:15A57
وصف الملف: application/pdf
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