Edge Degree Conditions for 2-Iterated Line Graphs to Be Traceable

Round 1

Reviewer 1 Report

In this work, the authors study the structure of a connected graph with a non-traceable 2-iterated line graph and give similar edge degree conditions of a connected graph to ensure its 2-iterated line graph to be traceable.

 

the paper lacks of effective comparisons with:

- Either the previous works of the authors*

- Or with similar works in order to show the effectiveness of the used method

Author Response

Dear Reviewer,

Thank you very much for refereeing our manuscript and for your comments! We considered your report completely, see the attached file. Hope it is fine for you. If you have furthermore comment, please tell us freely.

Sincerely yours

Liming Xiong for all coauthors

Author Response File: Author Response.pdf

Reviewer 2 Report

The authors of this paper studied the structure of a connected graph with a non-traceable 2-iterated line graph and provided similar edge degree conditions for a connected graph to ensure its 2-iterated line graph is traceable. There are some improvements and edits that need to be made to this paper:

 

1- Abstract must be very professional. The novelty of the work must be clearly needed in the abstract. Avoid usage of the same words more than once. However long sentences need to be avoided. Check the abstract clearly and rewrite it.

 

2- Contribution you have listed in the introduction looks very general. : The motivation of the paper should be clarified in the introduction part. The shortcoming of previous research should be fully analyzed.

 

3- Related work must discuss the existing methods with their advantages and disadvantages. You can modulate the one para about existing limitations and proposed ideology.

 

4- It is suggested that the authors read and cite these graph theoretic-based papers:

A) A fast divisive community detection algorithm based on edge degree betweenness centrality. Applied Intelligence. 2019 Feb;49(2):689-702.

B) Graph-based relevancy-redundancy gene selection method for cancer diagnosis. Computers in Biology and Medicine. 2022 Aug 1;147:105766.

C)  Graph theory and combinatorial calculus: An early approach to enhance robust understanding. ZDM–Mathematics Education. 2022 Aug 7:1-8.

 

5- The conclusion can be reviewed and modified. Implications for future research may also be included in the conclusion at the end.

Author Response

Dear reviewer, 

Thank for your comment for our manuscript, we have considered all your comments, please the attached file. If you have more comment and suggestion, please ask us freely.

Sincerely yours

Liming Xiong 

Author Response File: Author Response.pdf

Reviewer 3 Report

- Please clearly define the scope and purpose of the paper.

- Add a list of symbols used and their explanations, p is not defined.

- Theorem 3 and Figure 1 designations are not consistent

- Make an example demonstrating the application of the presented approach.  

Author Response

Dear Reviewer,

Thanks very much for your comments. We have considered all of your comments, see the attached file. If you have furthermore comment for this manuscript, please ask us freely.

Sincerely your

Liming Xiong for all authors

Author Response File: Author Response.pdf

Round 2

Reviewer 3 Report

I accept the article.