The G-Convexity and the G-Centroids of Composite Graphs

Round 1

Reviewer 1 Report

The author has studied the relationship between the g-centroids of composite graphs and their factors under various well-known graph operations such as graph Joins, Cartesian products, Prism, and the Corona. The work shows that the results will facilitate the academic community to focus on the factor graphs while designing an approximate algorithm for a composite graph as claimed. However, the graph needs some serious presentation correction. Some of the issue to mention a few are: 

1) Ending paragraph of the first section, the author can simply combine what work has been done in section, instead of explaining its subsection. 

2) While writing proposition, treat them as a distinct theorem or lemma, meaning mention the terminologies and considered used in the proposition rather than just result (Proposition 17). These corrections need to be done throughout the paper. 

3) Write the numbers for Remark, like Remark 2.1 instead of simple Remark: 
The reader can follow easily if there are any intext references/citations to the remark. 

4) As mentioned above, the presentation and format of the paper need serious attention. Please communicate with the editor to find the right format of the paper so that it will be easy for the reader to follow through. 

Please make these corrections and we will see the second round of the paper. Proof wise, the paper is scientifically sound. 

Author Response

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Author Response File: Author Response.pdf

Reviewer 2 Report

This paper presented the relationship between the g-centroids of composite graphs and their factors under various well-known graph operations such as graph Joins, Cartesian products, Prism, and the Corona.  In regard of the engineering applications, the g-convexity and the g-centroids of composite graphs are an important topic and can be of interest for Mathematics readership. Although the paper is well organized and is easy to follow the writing, some points in the manuscript need improvements or additions. To this reviewer, minor revisions and further clarifications are needed. The authors need to properly address the following comments to further improve this manuscript:

1.      Abstract possibly needs further improvements to address clearly the gap and contributions of the current study in comparison with the literature review.

2.      Introduction part: It's important to show some consistency in the current work. The gap of existing studies and the investigation of the current study should be consistent in-depth review.

Author Response

Please see the attachment.

Author Response File: Author Response.pdf

Reviewer 3 Report

See pdf attached.

Comments for author File: Comments.pdf

Author Response

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Author Response File: Author Response.pdf