Clar Covers of Overlapping Benzenoids: Case of Two Identically-Oriented Parallelograms

Round 1

Reviewer 1 Report

The manuscript entitled Clar covers of overlapping benzenoids: Case of two identically-oriented parallelograms by Henryk Witek * and Johanna Langner is a well presented computational research work.

The matematical language is well described;

The subjet is of interest for the community of chemists and related scientist that work in the field of symmetry at supramolecular level.

I am not a strong matematician, rather I am a synthetic chemist and it took time to me to fully undertand the complete picture but once undertood the reading of the manuscript was smooth.

Author Response

We thank the referee for reading our paper and giving favorable comments.

Reviewer 2 Report

The work by Witek and Langner is a thorough exploration of the graph theoretical constructs for expanded benzoidal shapes structures with application to chemistry. The work is dense at times, but the mathematical concepts certainly require this. As such, the paper is fitting for publication pending these below very minor corrections.

Some additional motivation for this work beyond its graph theoretical application would be useful. This could be a simple sentence explaining why large benzoidal structures are necessary to be explored in this way. Such large particles of carbon are no doubt important in combustion chemistry, astrochemistry, and materials science where graphene or polycyclic aromatic hydrocarbons are known or perceived to be crucial intermediates. Something to this effect should be stated.

The sentence beginning with “Unfortunately” on line 50 through line 53 is a bit of a run-on and should be broken up into at least 2 sentences.

A period is needed in Eq. 13 to signify the end of the previous sentence.

Line 219 should be a figure and not more text as should 229 and the others where images are plopped into the text.

Author Response

We thank the referee for his/her positive feedback on our manuscript. The comments of the referee has been taken into account in the preparation of the revised version of the manuscript. In particular, we have included the following modifications pertinent to the referee's comments:

• In introduction section, we have started our paper from the following sentence:
  
  Benzenoid hydrocarbons are an intensively-studied class of aromatic molecules attracting attention of scientists specializing in various fields of chemistry including organic synthesis and characterization,  combustion chemistry, nanoscience , atmospheric chemistry, astrochemistry, computational chemistry, and chemical graph theory.
  
  supported by 16 new recent citations illustrating our point. 
• The sentence starting with "Unfortunately" has been divided into 2 sentences, which should improve readability.
• A comma and a period have been added to Eq13.
• The figure in line 219 is a part of the sentence starting from line 217 and finishing in line 221, both grammatically and logically. We feel that converting this figure to a float and placing it at the bottom or at the top of this page will actually diminish the readability of this sentence. Therefore, if the SYMMETRY technical editor would allow for a non-float in the manuscript, we would prefer to keep this figure as a part of this sentence in the way it has been done in the original submission. Of course, if non-float figures are not acceptable for the journal, we conform to the suggestion of the referee. Similar remarks concern the non-float figures appearing in lines 229 and 234.

Reviewer 3 Report

Referee report for "Clar covers of overlapping benzenoids: Case of two
identically-oriented parallelograms".

In the paper, authors analyze all possible complex benzenoids that can be formed by overlapping two identically-oriented parallelograms. It turns out that some of them are Kekuléan and some are non-Kekuléan. Then, five families of Kekuléan structures are considered: parallelograms, generalized ribbons, horizontally overlapping parallelograms, intersecting parallelograms, and vertically overlapping parallelograms. As the main result, a complete set of closed-form formulas (in the form of multiple sums over binomial coefficients) for the ZZ polynomials of these classes are presented. In particular, three of the formulas are given with a proof based on the interface theory of benzenoids. However, the formulas for ZZ polynomials of intersecting parallelograms and horizontally overlapping parallelograms are given in
the form of conjectures (without a proof), verified by numerical tests. It is interesting that both conjectured formulas have the form of a determinant of dimension 2. It is believed that they will remain conjectures until an extension of John-Sachs theory applicable to Clar covers is developed.

In my opinion, the results are interesting and new. The paper is also very well written. Therefore, I can recommend it for publication in Symmetry. However, just some minor remarks have to be taken into account.

Minor remarks:
1. Page 2, line 9: it should be "... can be expressed..." instead of "... can expressed..."
2. Page 10, 11, 12: there are four figures which are not numbered. Probably it would be good to number them and mention them in the text.
3. Page 15, line 302: it should be "...proved in 1984...".
4. Page 16: I think that Figure 8 is not mentioned in the text.
5. Page 18, line 373: what means "fullereneZZ"?
6. Page 18, reference 3: journal name is written before the title.
7. Page 19, reference 32: it should be "Berli\v{c}" instead of "Berlic".

Author Response

We thank the referee for careful scrutiny of our manuscript and favorable comments. The referee's suggestions have been included in the revised version of our paper. In particular:

• The phrase "can" expressed is changed to "can be expressed"
• The figure on page 12 has been changed into a float figure (now Fig.7) and an appropriate caption has been added to it and it was mentioned in the text in the appropriate place. However, the three figures appearing on pages 10 and 11 constitute a inherent part of the sentences appearing before and after them, both gramatically and logically. We have chosen this type of text setup to facilitate understanding of the presented concept. If placement of such non-float figures is in accordance with the journal policy, we would like to retain these three figures in the current form.
• The referee is right that Figure 8 has not been mentioned in the text. We have corrected this omission.
• "by" is replaced by "in" in line 302
• The phrase "fullereneZZ" was produced by the LATEX command \reftitle{fullereneZZ}, which was wrong; we have changed it to \reftitle{ZZ polynomials of overlapping parallelograms} and we believe that a proper compilation of the LATEX file by the SYMMETRY editors will change it to a short title for our paper.
• In ref3 the journal and title were switched because in our .bib file we have erroneously switched the fields "journal" and "title"; we thank the referee for spotting this -otherwise very difficult to nitice- omission.
• The name Berlič is now spelled correctly