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Upper Bounds for the Isolation Number of a Matrix over Semirings

Author

Listed:
  • LeRoy B. Beasley

    (Department of Mathematics and Statistics, Utah State University, Logan, UT 84322-3900, USA)

  • Seok-Zun Song

    (Department of Mathematics, Jeju National University, Jeju 63243, Korea)

Abstract

Let S be an antinegative semiring. The rank of an m × n matrix B over S is the minimal integer r such that B is a product of an m × r matrix and an r × n matrix. The isolation number of B is the maximal number of nonzero entries in the matrix such that no two entries are in the same column, in the same row, and in a submatrix of B of the form b i , j b i , l b k , j b k , l with nonzero entries. We know that the isolation number of B is not greater than the rank of it. Thus, we investigate the upper bound of the rank of B and the rank of its support for the given matrix B with isolation number h over antinegative semirings.

Suggested Citation

  • LeRoy B. Beasley & Seok-Zun Song, 2019. "Upper Bounds for the Isolation Number of a Matrix over Semirings," Mathematics, MDPI, vol. 7(1), pages 1-6, January.
    • Handle: RePEc:gam:jmathe:v:7:y:2019:i:1:p:65-:d:196035
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