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Graph theory was originally introduced in computer science to study data structure. Chemists also introduced graph theory to study the relation between structure and properties for molecular compounds.

My questions: What are the typical applications of Chemical graph theory? What are some recent breakthroughs?

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This is a question that is answered by a straightforward literature search, here's e.g. two review papers from the 1980s:

as well as a more recent encyclopedia article Encyclopedia of Computational Chemistry 1998, pp. 1169-1190

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    $\begingroup$ Great answer. Can you add a short summary of the work following this answer format. $\endgroup$ – Thomas Jun 26 at 14:45
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I'd just briefly add that among other things, chemical graph theory is extensively used for computing so-called "molecular descriptors", which are used to capture some "common properties" of a certain class of molecules.

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Some recent work that comes to my mind is generation and analysis of fullerenes done by Peter Schwerdtfeger's group and described for example in

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    $\begingroup$ Could you provide a brief summary of how chemical graph theory is used in one of these papers? It will make the answer more complete for those who don't have easy access to the papers. $\endgroup$ – Tyberius Jun 26 at 14:51
  • $\begingroup$ I'll work on it. $\endgroup$ – LukasK Jun 30 at 15:08
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Too many references for me to elaborate on, but here's a recent example I like: "Graph Networks as a Universal Machine Learning Framework for Molecules and Crystals" in Chemistry of Materials.

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    $\begingroup$ Could you provide a brief summary of how chemical graph theory is used in this paper? It will make the answer more complete for those who don't have easy access to scientific journals. $\endgroup$ – Tyberius Jun 26 at 14:51
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This paper might be a good example: Chem, 4, 390-398 (2018)

Quoting the authors: 'Computer autonomously designs chemical syntheses of medicinally relevant molecules'.

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    $\begingroup$ Could you give a little more detail on how chemical graph theory is used in this paper? $\endgroup$ – Tyberius Jun 26 at 19:08
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Recently chemical graph theory has been used to give more physical and chemical insight on whether destructive quantum interference exists or not. Hope that helps. Let me know if I can help further.

Tsuji, Yuta, Ernesto Estrada, Ramis Movassagh, and Roald Hoffmann. "Quantum interference, graphs, walks, and polynomials." Chemical reviews 118, no. 10 (2018): 4887-4911.

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abed haidar is a new contributor to this site. Take care in asking for clarification, commenting, and answering. Check out our Code of Conduct.
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  • $\begingroup$ +1. Nice first answer, and welcome to our site !!! We hope to see much more of you here !!! I've informed Ramis Movassagh that you cited his paper :) $\endgroup$ – Nike Dattani Jul 1 at 3:15
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    $\begingroup$ Thank you very much ! Really happy to be here! My work was based on this paper so thank him for me :) $\endgroup$ – abed haidar Jul 1 at 3:47

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