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?
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
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.
Todescini and Consonni, Molecular Descriptors for Chemoinformatics already a bit dated, offers an extensive collection of 5000+ descriptors.
Prof. Ivan Gutman's list of publications would be a worthwhile reference collection.
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
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.
This paper might be a good example: Chem, 4, 390-398 (2018)
Quoting the authors: 'Computer autonomously designs chemical syntheses of medicinally relevant molecules'.
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.
