Upper Bounds for the Isolation Number of a Matrix Over Semirings

Authors

LeRoy B. Beasley, Utah State UniversityFollow
Seok-Zun Song, Jeju National University

Document Type

Article

Journal/Book Title/Conference

Mathematics

Volume

7

Issue

1

Publisher

MDPI

Publication Date

1-9-2019

First Page

1

Last Page

6

Creative Commons License

This work is licensed under a Creative Commons Attribution 4.0 License.

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_k,j

b_i,l 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.

Recommended Citation

Beasley, L.B.; Song, S.-Z. Upper Bounds for the Isolation Number of a Matrix over Semirings. Mathematics 2019, 7, 65.