Upper Bounds for the Isolation Number of a Matrix over Semirings
Round 1
Reviewer 1 Report
In the manuscript, the authors study the possible values of the rank of a matrix B and the rank of the support of it for a given isolation number k over antinegative semirings. The authors show that, if the isolation number is greater than 2, there exist cases when the Boolean rank of the support may be strictly greater than the isolation number of B. The authors also show that there exist cases when the Boolean rank of the support is equal to the isolation number of the matrix B. Moreover, the authors prove that, for isolation numbers 1 and 2, the isolation number of B is the same as the Boolean rank of the support of it.
The topic of the manuscript is interesting, but the results are not very strong. The main result is limited to isolation numbers 1 and 2. The rest of the results are more or less examples only. However, as there are many application areas for this type of results, I still recommend to accept the manuscript for publication. Since the manuscript is well-written and requiring stronger results would not be fair, I recommend to accept the manuscript for publication after a minor revision only. Just please check the paper for typos once more. I spotted couple of small typos.
Author Response
Thank you for the recommendation to be published !
We also thank you for your some commnets.
We revised our paper according to your comments such as some typo errors and some expressions.
Reviewer 2 Report
Please see the attached file.
Comments for author File: 
Comments.pdf
Author Response
Thank you for your comments on our paper !
We wrote our thanks for your many helpful comments in the Acknoldgements.
I submit the revised versin of our paper. And I attach a pdf-file which shows revisions according to each your comment. At there, you can check the pages and lines in the revised version.
I and my co-author appreciate you deeply for your all the comments.
Please check our revision.
We also check the English expressions by the native American, my co-author.
Author Response File: Author Response.pdf
