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The Bipartite Zero Forcing Set for a Full Sign Pattern Matrix

Author

Listed:
  • Gu-Fang Mou

    (College of Mathematics and Information Science, Leshan Normal University, Leshan 614000, Sichuan, China)

  • Tian-Fei Wang

    (College of Mathematics and Information Science, Leshan Normal University, Leshan 614000, Sichuan, China)

  • Zhong-Shan Li

    (Department of Mathematics and Statistics, Georgia State University, Atlanta, GA 30302-4110, USA)

Abstract

For an m × n sign pattern P , we define a signed bipartite graph B ( U , V ) with one set of vertices U = { 1 , 2 , … , m } based on rows of P and the other set of vertices V = { 1 ′ , 2 ′ , … , n ′ } based on columns of P . The zero forcing number is an important graph parameter that has been used to study the minimum rank problem of a matrix. In this paper, we introduce a new variant of zero forcing set−bipartite zero forcing set and provide an algorithm for computing the bipartite zero forcing number. The bipartite zero forcing number provides an upper bound for the maximum nullity of a square full sign pattern P . One advantage of the bipartite zero forcing is that it can be applied to study the minimum rank problem for a non-square full sign pattern.

Suggested Citation

  • Gu-Fang Mou & Tian-Fei Wang & Zhong-Shan Li, 2020. "The Bipartite Zero Forcing Set for a Full Sign Pattern Matrix," Mathematics, MDPI, vol. 8(3), pages 1-14, March.
    • Handle: RePEc:gam:jmathe:v:8:y:2020:i:3:p:354-:d:329041
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    References listed on IDEAS

    as
    1. Maguy TREFOIS & Jean-Charles DELVENNE, 2015. "Zero forcing number, constrained matchings and strong structural controllability," LIDAM Reprints CORE 2785, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
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