A Complete Characterization of Bipartite Graphs with Given Diameter in Terms of the Inverse Sum Indeg Index

Round 1

Reviewer 1 Report

The paper under review characterizes the bipartite graphs having the largest, second largest, as well as lowest inverse sum indeg index. The results are to the best of my knowledge new and correct. Therefore, I recommend its publication after one minor suggestion. Recently, a number of papers dealing with ISI have appeared. I recommend authors cite some of the most recent papers to show the actuality of the investigated index. Some of the papers that should be cited are:

[*] Jiang, Yisheng, Xiaodan Chen, and Wenshui Lin. "A note on chemical trees with maximal inverse sum indeg index." MATCH Commun. Math. Comput. Chem. 86 (2021): 29-38.

[*] Lin, W., Fu, P., Zhang, G., Hu, P., & Wang, Y. (2022). On two conjectures concerning trees with maximal inverse sum indeg index. Computational and Applied Mathematics, 41(6), 1-8.

[*] Balachandran, Selvaraj, Suresh Elumalai, and Toufik Mansour. "A short note on inverse sum indeg index of graphs." Asian-European Journal of Mathematics 14.01 (2021): 2050152.

Author Response

Dear Reviewer,

On behalf of all the contributing authors, I would like to express our sincere appreciations of your letter and reviewers’ constructive comments concerning our article entitled "A complete characterization of bipartite graphs with given diameter in terms of the inverse sum indeg index" (Manuscript No.: axioms-2025904). These comments are all valuable and helpful for improving our article. According to the assistant editor and reviewers’ comments, we have made extensive modifications to our manuscript to make our results convincing. The following are the corresponding corrections.

[1] We have added the following three references to support our manuscript:

--S. Balachandran, S. Elumalai, T. Mansour, A short note on inverse sum indeg index of graphs, Asian-European Journal of Mathematics, 14 (2021) 2050152.

--Y. Jiang, X. Chen, W. Lin, A note on chemical trees with maximal inverse sum indeg index, MATCH Commun. Math. Comput. Chem., 86 (2021) 29-38.

--W. Lin, P. Fu, G. Zhang, P. Hu, Y. Wang, On two conjectures concerning trees with maximal inverse sum indeg index，Computational and Applied Mathematics, 41(6) (2022) 1-8.

[2] We have carefully checked the manuscript and corrected the errors accordingly. For example, we have corrected "wide applications" to be "wide range of applications" in the Abstract Section and Section 1. Besides, we have checked and corrected the singular and plural of nouns throughout of the manuscript.

Looking forward to getting some good news or valuable suggestions from you.

Best wishes

Guifu Su

Reviewer 2 Report

I believe the results are correct and interesting. The presentation is ok, some minor improvements are needed for the paper to be publishable, for example, single vs. plurals, "wide range of applications", not "wide applications" etc. 

Author Response

Dear Reviewer,

On behalf of all the contributing authors, I would like to express our sincere appreciations of your letter and reviewers’ constructive comments concerning our article entitled "A complete characterization of bipartite graphs with given diameter in terms of the inverse sum indeg index" (Manuscript No.: axioms-2025904). These comments are all valuable and helpful for improving our article. According to the assistant editor and reviewers’ comments, we have made extensive modifications to our manuscript to make our results convincing. The following are the corresponding corrections.

[1] We have added the following three references to support our manuscript:

--S. Balachandran, S. Elumalai, T. Mansour, A short note on inverse sum indeg index of graphs, Asian-European Journal of Mathematics, 14 (2021) 2050152.

--Y. Jiang, X. Chen, W. Lin, A note on chemical trees with maximal inverse sum indeg index, MATCH Commun. Math. Comput. Chem., 86 (2021) 29-38.

--W. Lin, P. Fu, G. Zhang, P. Hu, Y. Wang, On two conjectures concerning trees with maximal inverse sum indeg index，Computational and Applied Mathematics, 41(6) (2022) 1-8.

[2] We have carefully checked the manuscript and corrected the errors accordingly. For example, we have corrected "wide applications" to be "wide range of applications" in the Abstract Section and Section 1. Besides, we have checked and corrected the singular and plural of nouns throughout of the manuscript.

Looking forward to getting some good news or valuable suggestions from you.

Best wishes

Guifu Su