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## The nonnegative Q−matrix completion problem

#### Bhaba Kumar SARMA [1] , Kalyan SİNHA [2]

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.
Digraph, Partial matrix, Matrix completion, Nonnegative Q-matrix, Q-completion problem
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 Bibtex @research article { jacodesmath284563, journal = {Journal of Algebra Combinatorics Discrete Structures and Applications}, issn = {}, eissn = {2148-838X}, address = {}, publisher = {Yildiz Technical University}, year = {2017}, volume = {4}, pages = {61 - 74}, doi = {10.13069/jacodesmath.05630}, title = {The nonnegative Q−matrix completion problem}, key = {cite}, author = {Sarma, Bhaba Kumar and Si̇nha, Kalyan} } APA Sarma, B , Si̇nha, K . (2017). The nonnegative Q−matrix completion problem . Journal of Algebra Combinatorics Discrete Structures and Applications , 4 (1) , 61-74 . DOI: 10.13069/jacodesmath.05630 MLA Sarma, B , Si̇nha, K . "The nonnegative Q−matrix completion problem" . Journal of Algebra Combinatorics Discrete Structures and Applications 4 (2017 ): 61-74 Chicago Sarma, B , Si̇nha, K . "The nonnegative Q−matrix completion problem". Journal of Algebra Combinatorics Discrete Structures and Applications 4 (2017 ): 61-74 RIS TY - JOUR T1 - The nonnegative Q−matrix completion problem AU - Bhaba Kumar Sarma , Kalyan Si̇nha Y1 - 2017 PY - 2017 N1 - doi: 10.13069/jacodesmath.05630 DO - 10.13069/jacodesmath.05630 T2 - Journal of Algebra Combinatorics Discrete Structures and Applications JF - Journal JO - JOR SP - 61 EP - 74 VL - 4 IS - 1 SN - -2148-838X M3 - doi: 10.13069/jacodesmath.05630 UR - https://doi.org/10.13069/jacodesmath.05630 Y2 - 2020 ER - EndNote %0 Journal of Algebra Combinatorics Discrete Structures and Applications The nonnegative Q−matrix completion problem %A Bhaba Kumar Sarma , Kalyan Si̇nha %T The nonnegative Q−matrix completion problem %D 2017 %J Journal of Algebra Combinatorics Discrete Structures and Applications %P -2148-838X %V 4 %N 1 %R doi: 10.13069/jacodesmath.05630 %U 10.13069/jacodesmath.05630 ISNAD Sarma, Bhaba Kumar , Si̇nha, Kalyan . "The nonnegative Q−matrix completion problem". Journal of Algebra Combinatorics Discrete Structures and Applications 4 / 1 (January 2017): 61-74 . https://doi.org/10.13069/jacodesmath.05630 AMA Sarma B , Si̇nha K . The nonnegative Q−matrix completion problem. Journal of Algebra Combinatorics Discrete Structures and Applications. 2017; 4(1): 61-74. Vancouver Sarma B , Si̇nha K . The nonnegative Q−matrix completion problem. Journal of Algebra Combinatorics Discrete Structures and Applications. 2017; 4(1): 61-74.