Extended Graph of Fuzzy Topographic Topological Mapping Model: ${\mathit{G}}_{\mathbf{0}}^{\mathbf{4}}\left({\mathit{F}\mathit{T}\mathit{T}\mathit{M}}_{\mathit{n}}^{\mathbf{4}}\right)$

Round 1

Reviewer 1 Report

Comments for author File: Comments.pdf

Author Response

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Reviewer 2 Report

In this manuscripts authors introduced many topological properties of fuzzy graphs. Some results have been discussed here. But, minor rivisions are needed... 

Write the abstract in more details, some results are not clear in abstract. More discussion are needed, some theorems are introduced, but explanation is not given. Introduction is too short, cite some recent works 1. Estimation of most effected cycle and internet network route based on complexity function of graph in fuzzy environment, Artificial intelligence review, 2. Randic index of bipolar fuzzy graphs and their applications, journal of applied mathematics and computing. Discuss some results. Write some limitations of the work in conclusion section. Also, give some future works. 

Author Response

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Reviewer 3 Report

First of all, I would like to congratulate the authors on the manuscript as they present a novel approach to this type of model. Thus, I believe that the article can be improved in the following aspects:
1. Write abstract in a more claiming manner by highlighting your contribution.
2. Please recheck all your derivations meticulously.
3. Have you used any software for evaluation of the derived or proposed equations?
4. No comparative study is shown. It is mandatory to show some comparative graphs and tables to claim about the improvement of your method.
5. Figures etc. should be made more clear and visible.
6. Please correct all grammatical errors which are plenty in numbers.
7. Please check the reference list and delete the less relevant ones and add few more relevant ones.
8. Rewrite conclusion in a precise way.
9. Add separate subheading for discussions.

10. Also mention some areas of applications

Author Response

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Round 2

Reviewer 1 Report

My Comments

The paper brings new idea of “Extended Graph of Fuzzy Topographic Topological Mapping 2 Model: ?? ? (????? ? )” never studied before, upon the best of my knowledge, that’s why the paper is worth.

Major corrections:

                               I.            The first letter of the Keywords must be capital.

                            II.            “Fuzzy Topographic Topological Mapping (FTTM)…” should be fuzzy topographic topological mapping (FTTM)

                         III.            Remove the space between line 127 and 128.

                         IV.            The introduction section needs some recent literature review to be added.

                            V.            “Originally, the model is a 4-tuple of topological spaces and mappings and its respective homeomorphic mappings [4].“ should be “Originally, the model is a 4-tuple of topological spaces and mappings of its respective homeomorphic mappings [4].”

                         VI.            Add period at the end of this line “The FTTM is defined formally as follows (see Fig- 31 ure 1)”

                      VII.            Add period at the end of line 38.

                   VIII.            Add comma at the end of line 62

                         IX.            Add some more recent references.

 

                            X.            All references need to be uniform.

Author Response

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Reviewer 3 Report

It can be accepted now.

Author Response

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Author Response File: Author Response.pdf

Round 3

Reviewer 1 Report

All the suggestions are incorporated.