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The nonnegative Q−matrix completion problem

Yıl 2017, , 61 - 74, 11.01.2017
https://doi.org/10.13069/jacodesmath.05630

Öz

In this paper, the nonnegative $Q$-matrix completion problem is studied. A real $n\times n$ matrix is a $Q$-matrix if for $k\in \{1,\ldots, n\}$, the sum of all $k \times k$ principal minors is positive. A digraph $D$ is said to have nonnegative $Q$-completion if every partial nonnegative $Q$-matrix specifying $D$ can be completed to a nonnegative $Q$-matrix. For nonnegative $Q$-completion problem, necessary conditions and sufficient conditions for a digraph to have nonnegative $Q$-completion are obtained. Further, the digraphs of order at most four that have nonnegative $Q$-completion have been studied.

Kaynakça

  • [1] G. Chartrand, L. Lesniak, Graphs and Digraphs, Fourth Edition, Chapman & Hall/CRC, London, 2005.
  • [2] J. Y. Choi, L. M. DeAlba, L. Hogben, B. Kivunge, S. Nordstrom, M. Shedenhelm, The nonnegative P_0−matrix completion problem, Electron. J. Linear Algebra 10 (2003) 46–59.
  • [3] J. Y. Choi, L. M. DeAlba, L. Hogben, M. S. Maxwell, A. Wangsness, The P_0−matrix completion problem, Electron. J. Linear Algebra 9 (2002) 1–20.
  • [4] L. M. Dealba, L. Hogben, B. K. Sarma, The Q−matrix completion problem, Electron. J. Linear Algebra 18 (2009) 176–191.
  • [5] S. M. Fallat, C. R. Johnson, J. R. Torregrosa, A. M. Urbano, P−matrix completions under weak symmetry assumptions, Linear Algebra Appl. 312(1–3) (2000) 73–91.
  • [6] F. Harary, Graph Theory, Addison-Wesley, Reading, MA, 1969.
  • [7] L. Hogben, Graph theoretic methods for matrix completion problems, Linear Algebra Appl. 328(1–3) (2001) 161–202.
  • [8] L. Hogben, Matrix completion problems for pairs of related classes of matrices, Linear Algebra Appl. 373 (2003) 13–29.
  • [9] L. Hogben, A. Wangsness, Matrix completion problems, in Handbook of Linear Algebra, L. Hogben, Editor, Chapman and Hall/CRC Press, Boca Raton, 2007.
  • [10] C. R. Johnson, B. K. Kroschel,The combinatorially symmetric P−matrix completion problem, Electron. J. Linear Algebra 1 (1996) 59–63.
  • [11] C. Jordon, J. R. Torregrosa, A. M. Urbano, Completions of partial P−matrices with acyclic or non–acyclic associated graph, Linear Algebra Appl. 368 (2003) 25–51.
Yıl 2017, , 61 - 74, 11.01.2017
https://doi.org/10.13069/jacodesmath.05630

Öz

Kaynakça

  • [1] G. Chartrand, L. Lesniak, Graphs and Digraphs, Fourth Edition, Chapman & Hall/CRC, London, 2005.
  • [2] J. Y. Choi, L. M. DeAlba, L. Hogben, B. Kivunge, S. Nordstrom, M. Shedenhelm, The nonnegative P_0−matrix completion problem, Electron. J. Linear Algebra 10 (2003) 46–59.
  • [3] J. Y. Choi, L. M. DeAlba, L. Hogben, M. S. Maxwell, A. Wangsness, The P_0−matrix completion problem, Electron. J. Linear Algebra 9 (2002) 1–20.
  • [4] L. M. Dealba, L. Hogben, B. K. Sarma, The Q−matrix completion problem, Electron. J. Linear Algebra 18 (2009) 176–191.
  • [5] S. M. Fallat, C. R. Johnson, J. R. Torregrosa, A. M. Urbano, P−matrix completions under weak symmetry assumptions, Linear Algebra Appl. 312(1–3) (2000) 73–91.
  • [6] F. Harary, Graph Theory, Addison-Wesley, Reading, MA, 1969.
  • [7] L. Hogben, Graph theoretic methods for matrix completion problems, Linear Algebra Appl. 328(1–3) (2001) 161–202.
  • [8] L. Hogben, Matrix completion problems for pairs of related classes of matrices, Linear Algebra Appl. 373 (2003) 13–29.
  • [9] L. Hogben, A. Wangsness, Matrix completion problems, in Handbook of Linear Algebra, L. Hogben, Editor, Chapman and Hall/CRC Press, Boca Raton, 2007.
  • [10] C. R. Johnson, B. K. Kroschel,The combinatorially symmetric P−matrix completion problem, Electron. J. Linear Algebra 1 (1996) 59–63.
  • [11] C. Jordon, J. R. Torregrosa, A. M. Urbano, Completions of partial P−matrices with acyclic or non–acyclic associated graph, Linear Algebra Appl. 368 (2003) 25–51.
Toplam 11 adet kaynakça vardır.

Ayrıntılar

Konular Mühendislik
Bölüm Makaleler
Yazarlar

Bhaba Kumar Sarma Bu kişi benim

Kalyan Sinha

Yayımlanma Tarihi 11 Ocak 2017
Yayımlandığı Sayı Yıl 2017

Kaynak Göster

APA Sarma, B. K., & Sinha, K. (2017). The nonnegative Q−matrix completion problem. Journal of Algebra Combinatorics Discrete Structures and Applications, 4(1), 61-74. https://doi.org/10.13069/jacodesmath.05630
AMA Sarma BK, Sinha K. The nonnegative Q−matrix completion problem. Journal of Algebra Combinatorics Discrete Structures and Applications. Ocak 2017;4(1):61-74. doi:10.13069/jacodesmath.05630
Chicago Sarma, Bhaba Kumar, ve Kalyan Sinha. “The Nonnegative Q−matrix Completion Problem”. Journal of Algebra Combinatorics Discrete Structures and Applications 4, sy. 1 (Ocak 2017): 61-74. https://doi.org/10.13069/jacodesmath.05630.
EndNote Sarma BK, Sinha K (01 Ocak 2017) The nonnegative Q−matrix completion problem. Journal of Algebra Combinatorics Discrete Structures and Applications 4 1 61–74.
IEEE B. K. Sarma ve K. Sinha, “The nonnegative Q−matrix completion problem”, Journal of Algebra Combinatorics Discrete Structures and Applications, c. 4, sy. 1, ss. 61–74, 2017, doi: 10.13069/jacodesmath.05630.
ISNAD Sarma, Bhaba Kumar - Sinha, Kalyan. “The Nonnegative Q−matrix Completion Problem”. Journal of Algebra Combinatorics Discrete Structures and Applications 4/1 (Ocak 2017), 61-74. https://doi.org/10.13069/jacodesmath.05630.
JAMA Sarma BK, Sinha K. The nonnegative Q−matrix completion problem. Journal of Algebra Combinatorics Discrete Structures and Applications. 2017;4:61–74.
MLA Sarma, Bhaba Kumar ve Kalyan Sinha. “The Nonnegative Q−matrix Completion Problem”. Journal of Algebra Combinatorics Discrete Structures and Applications, c. 4, sy. 1, 2017, ss. 61-74, doi:10.13069/jacodesmath.05630.
Vancouver Sarma BK, Sinha K. The nonnegative Q−matrix completion problem. Journal of Algebra Combinatorics Discrete Structures and Applications. 2017;4(1):61-74.