k-Zero-Divisor and Ideal-Based k-Zero-Divisor Hypergraphs of Some Commutative Rings
Round 1
Reviewer 1 Report
In the related paper, they showed that two commutative rings so that one of them induces a family of complete k-zero-divisor hypergraphs while another one induces a family of k-partite σ-zero-divisor hypergraphs.
Then the authors determined the diameter and the minimum length of all cycles of the family of k-partite σ-zero-divisor hypergraphs.
They gave the definition of an ideal-based k-zero-divisor hypergraph as well as a k-zero-divisor hypergraph, and then investigated some basic results on these hypergraphs concerning a k-partite k-uniform hypergraph, a complete k-uniform hypergraph and a clique.
The results are correct and original. The English of this paper is acceptable.
This paper will be recommended for publication after some revisions.
- There are little grammar errors and punctuation. So, the author have to check this manuscript word by word for grammar errors and punctuation.
- To improve the manuscript, they can support their results with more examples and they can give more explanations of their results and examples.
Author Response
Thank you very much for great comments. We have checked the whole manuscript word by word for grammar errors and punctuation. We also have added Example 3 for supporting Theorem 6, Example 4 for supporting Theorem 8 and Example 5 for supporting Theorem 9, please see page 11 line 443, Page 11 line 468 and page 12 line 499, respectively of our revised manuscript. For more detail, please see the pdf file attached.
Author Response File: 
Author Response.pdf
Reviewer 2 Report
In the attached document you can find my reviewer report.
Comments for author File: Comments.pdf
Author Response
Thank you for great comments. We have changed to use the term "girth" according to the suggestion and also searched and made changes all places necessary. For more detail, please see the pdf file attached.
Author Response File: Author Response.pdf
Reviewer 3 Report
Manuscript Title: $k$-Zero-Divisor and Ideal-Based $k$-Zero-Divisor Hypergraphs of Some Commutative Rings
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Manuscript ID: symmetry-1406879
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Authors: Pinkaew Siriwong and Ratinan Boonklurb
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Comments: In this paper, the authors study the $k$-zero-divisor and ideal-based $k$-zero-divisor hypergraphs and their properties of some commutative rings. The main results are of some interest and the proofs of main theorems are correct. However, there are some writing errors. So I recommend it accept for publication with some minor revision. My detailed comments are as follows.
\begin{enumerate}
\item page 2, line 54, I suggest the latter "where" change into ",".
\item page 3, line 101, Add a period at the end.
\item page 3, line 109, Add a period befor "Then".
\item page 4, line 141, Add a ")" before ", is"
\item page 4, line 156, "tedious" is miss-spelled.
\item page 5, line 191, change "element" into "elements".
\item page 5, line 202, Delete one "and".
\item page 6, line 218, Add a "," between "$\overline{21}$" and "$\overline{55}$".
\item page 6, line 230, "hyperedges" $\rightarrow$ "hyperedge".
\item page 6, line 241, "cycle" $\rightarrow$ "cycles".
\item page 7, line 265, "a" $\rightarrow$ "an".
\item page 8 and page 9, check whether it is "$R\setminus I$" or $R/ I$.
\item page 9, line 350, Add a period at the end.
\item page 9, line 363, "products" $\rightarrow$ "product".
\item page 10, line 418, "contradict" $\rightarrow$ "contradicts".
\end{enumerate}
Comments for author File: Comments.pdf
Author Response
Thank you very much for great comments. We have changed according to your suggestions. For more detail, please see the pdf file attached.
Author Response File: Author Response.pdf
