0
$\begingroup$

In my last question ( Numbering in a derivative of azulene ), I asked about the numbered of a molecule in order to find the Vertex Adjacency Matrix (VAM) of the same molecule. To explain my question properly, I will do my best to show my effort from A to Z as follows: In general in order to find the VAM we use the formalism described by VAM formalism To apply it onto the molecule I am studying, I first applied it to azulene and with agreement with the paper Quantum Interference, Graphs, Walks, and Polynomials the VAM represented by A is: VAM for azulene only

Now by having the correct numbering to my molecule (Numbering in a derivative of azulene), it also should be a 10 x 10 matrix. The difference is instead of hydrogen we now have Oxygen and hydrogen Sulfide involved in positions 1,5 and 2,6 as shown: Finding the VAM for this molecule

To find VAM the only way was to study the VAM of weighted Graphs as shown below: VAM for weighted graphs

Here are my questions: 1- Should I include the parameter h only for the weighted carbons since the numbering of the molecule I am studying includes only carbon? 2- If 1 is no, how should I include the k parameters described before hand?

Any other suggestions to find VAM is appreciated.

$\endgroup$
0
$\begingroup$

As a comment: The matrix-representation you search emerges from graph theory, and mathematics. The numbers drawn in the structures earlier (1 for the carbonyl carbon, 2 to the carbon adjacent to the -SH group) a synthetic chemist refers to (e.g., "let us introduce an alkyl chain in the 4-position") do not (necessarily) relate to the numbers to denote the vertices in these nets. These are seasoned descriptions are still reviewed (2nd edition), and apparently the Open Molecular Generator were one tool to generate them.

$\endgroup$
  • $\begingroup$ I have two questions: 1- Should I not have asked here and asked in the maths section? 2- Would you be able to elaborate more from a chemist perspective on the relationship between numbers and vertices denotation? $\endgroup$ – abed haidar Dec 5 '18 at 3:47
  • $\begingroup$ @abedhaidar Re #1: It is not wrong to ask at ChemSE, or math; the question is at the interface between the two (like Chemometrics) or even a third (Cheminformatics). I speculate contacting a not-only-pure-chemistry research group might be beneficial (e.g., Spackman, crystalexplorer.scb.uwa.edu.au/index.html; or even Hutchinson, hutchison.chem.pitt.edu, because of his contributions to openbabel). #2: The numbering in the chemical structures follows the priniciple to spot a "parental" core structure, oriented on the canvas according to rules, and numbered according to others. $\endgroup$ – Buttonwood Dec 5 '18 at 8:51
  • $\begingroup$ @abedhaidar (Part 2) Then, if there are chains, they are seen like decoration, with their own set of numbering (again a set of rules), eventually merged to the core structure while retaining their (inner) numbering. Which is why an organic chemist would count 1 to 4 within the square (top most structure 3--6), once to 1 (for the branch 6--7, a methyl group), and once 1 to 2 (for the branch 3-2-1, an ethyl group) and say 1-ethyl-2-methyl-cyclobutane. The matrix reminded me a bit to the connection tables seen e.g. in MDL's mol2 files (but, CT are not these matrices), that's all I can say here. $\endgroup$ – Buttonwood Dec 5 '18 at 9:05

Your Answer

By clicking "Post Your Answer", you acknowledge that you have read our updated terms of service, privacy policy and cookie policy, and that your continued use of the website is subject to these policies.

Not the answer you're looking for? Browse other questions tagged or ask your own question.