A. Y. Alfakih

Books:

• A. Y. Alfakih , Euclidean Distance Matrices and Their Applications in Rigidity Theory.
  ISBN 978-3-319-97845-1 and ISBN 978-3-319-97846-8 . Springer, (2018)

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Completed or Submitted Papers:

• A. Y. Alfakih , On The Colin de Verdiere Graph Number and Penny Graphs. . arXiv 2006.05197

• A. Y. Alfakih , On Theorems of Sinajova, Rankin and Kuperberg Concerning Spherical Point Configurations. . arXiv 1908.00881

• A. Y. Alfakih , On stress matrices of chordal frameworks in general position. . arXiv 1205.3990

• A. Y. Alfakih , A remark on the Manhattan distance matrix of a rectangular grid. . arXiv 1208.5150

Published Papers:

• A. Y. Alfakih , On unit spherical Euclidean distance matrices which differ in one entry.
  Linear Algebra Appl. Vol 594, 29--50 (2020)

• A. Y. Alfakih , On representations of graphs as two-distance sets.
  Discrete Math. Vol 343, 111587 (2020)

• A. Y. Alfakih , On yielding and jointly yielding entries of Euclidean distance matrices.
  Linear Algebra Appl. Vol 556, 144--161 (2018)

• A. Y. Alfakih , On dimensional and universal rigidties of bar frameworks.
  In Handbook of Geometric Constraint Systems Principles.
  M. Sitharam, A. St.John and J. Sidman Editors. CRC Press, Taylor & Francis (2018)

• A. Y. Alfakih , Graph connectivity and universal rigidity of bar frameworks.
  Disc. Appl. Math. Vol 217, 707--710 (2017)

• A. Y. Alfakih , Universal rigidity of bar frameworks via the geometry of spectrahedra.
  J. Global Optim. Vol 67, 909--924 (2017).

• A. Y. Alfakih , On Farkas lemma and dimensional rigidity of bar frameworks. .
  Linear Algebra Appl. Vol 486, 504--522 (2015)

• A. Y. Alfakih , Local, dimensional and universal rigidities: A unified Gram matrix approach.
  In Rigidity and Symmetry. R. Connelly, W. Whiteley and A. Weiss Editors. Fields Institute Communications, Vol=70, pages 41--60.
  Springer, (2014)

• A. Y. Alfakih and V-H Nguyen , On affine motions and universal rigidity of tensegrity frameworks. .
  Linear Algebra Appl. Vol 439, 3134--3147 (2013)

• A. Y. Alfakih and Y. Ye , On affine motions and bar frameworks in general positions. .
  Linear Algebra Appl. vol 438, 31--36, (2013)

• A. Y. Alfakih, N. Taheri and Y. Ye , On stress matrices of (d+1)-lateration frameworks in general position. .
  Math. Program. vol 137, 1--17, (2013)

• A. Y. Alfakih , Universal rigidity of bar frameworks in general position: A Euclidean distance matrix approach.
  In Distane geometry, theory, methods and applications. A. Mucherino, C. Lavor, L. Liberti and N. Maculan Editors. pages 3--22.
  Springer, (2013)

• A. Y. Alfakih, On bar frameworks, stress matrices and semidefinite programming .
  Math. Program. Ser. B. Vol 129, 113--128, (2011)

• A. Y. Alfakih, On the universal rigidity of generic bar frameworks.
  Contribution Disc. Math. vol 5, no 1, 7--17, (2010)

• A. Y. Alfakih, On the dual rigidity matrix.
  Linear Algebra Appl. 428, 962--972, (2008).

• A. Y. Alfakih, On the eigenvalues of Euclidean distance matrices.
  Comput. Appl. Math. Vol 27, no 3, 237--250, (2008)

• A. Y. Alfakih and H. Wolkowicz, Some necessary and some sufficient trace inequalities for Euclidean distance matrices.
  Linear Mult. Algebra . 55, 499--506, (2007).

• A. Y. Alfakih, On dimensional rigidity of joint-and-bar frameworks.
  Discrete Appl. Math. 155, 1244-1253, (2007).

• A. Y. Alfakih, On the nullspace, the rangespace and the characteristic polynomial of Euclidean distance matrices.
  Linear Algebra Appl. . 416, 348-354, (2006).

• A. Y. Alfakih, A remark of the faces of the cone of Euclidean Distance Matrices.
  Linear Algebra Appl. . 414, 266-270, (2006).

• A. Y. Alfakih, On the Uniqueness of Euclidean Distance Matrix Completions: the case of points in general position.
  Linear Algebra Appl. ., 397, 265-277 (2005).

• A. Y. Alfakih and H. Wolkowicz, Two Theorems on Euclidean Distance Matrices and Gale Transform.
  Linear Algebra Appl. ., 340, 149--154 (2002).

• A. Y. Alfakih, On Rigidity and Realizability of Weighted Graphs.
  Linear Algebra Appl. , 325, 57--70 (2001).

• A. Y. Alfakih, Graph Rigidity via Euclidean Distance Matrices.
  Linear Algebra Appl. ., 310, 149--165 (2000).

• A. Y. Alfakih, T. Yi and K. G. Murty, Some Facets of an Assignment Problem with a 0--1 Side Constraint.
  J. of Comb. Optim. , 4, 365--388 (2000).

• A. Y. Alfakih and H. Wolkowicz, Matrix Completion Problems.
  In Handbook of Semidefinite Programming: Theory, Algorithms, and Applications. H. Wolkowicz, R. Saigal, and L. Vandenberghe editors, Kluwer Academic Publishers, Boston. pp 533--546 (2000).

• A. Y. Alfakih, A. Khandani and H. Wolkowicz, Solving Euclidean Distance Matrix Completion Problems via Semidefinite Programming.
  Comput. Optim. Appl. , 12, 13--30 (1999).

• A. Y. Alfakih and K. G. Murty, Adjacency on the Constrained Assignment Problem.
  Discrete Appl. Math. , 87, 269--274 (1998).