Zero forcing parameters and minimum rank problems

By Francesco Barioli, Wayne W. Barrett, Shaun M. Fallat, H. Tracy Hall, Leslie Hogben, Bryan L. Shader, Pauline van den Driessche, H. Holst. 2010

237 citations recorded by the source corpus.

The zero forcing number Z(G), which is the minimum number of vertices in a zero forcing set of a graph G, is used to study the maximum nullity/minimum rank of the family of symmetric matrices described by G. It is shown that for a connected graph of order at least two, no vertex is in every zero forcing set. The positive semidefinite zero forcing number Z+(G) is introduced, and shown to be equal to |G|-OS(G), where OS(G) is the recently defined ordered set number that is a lower bound for minimum positive semidefinite rank. The positive semidefinite zero forcing number is applied to the computation of positive semidefinite minimum rank of certain graphs. An example of a graph for which the real positive symmetric semidefinite minimum rank is greater than the complex Hermitian positive semidefinite minimum rank is presented.

Subfields: Computational Theory and Mathematics, Geometry and Topology

View Paper: https://www.semanticscholar.org/paper/35b616c943c4d071463aeb2405d1bc559f49a396

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In Computational Theory and Mathematics

  1. Darren D. Row
  2. Leslie Hogben
  3. My Huynh
  4. Joshua C. LaGrange
  5. Christina Edholm
  6. Shaun M. Fallat
  7. Samet Oymak
  8. Necmiye Ozay

In Geometry and Topology

  1. Darren D. Row
  2. Leslie Hogben
  3. Shaun M. Fallat
  4. Samet Oymak
  5. Necmiye Ozay

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