Hi Simon, I'd think that one place to start would be Carl Borchardt's 1860 proof of what became known as Cayley's Formula.
Thank you Phillip . Iam interested to know the first few research papers in graph theory. Euler proved that there is no solution for Konigsberg bridge problem and that was the first paper. Who is the follower of Euler?. I came to know that the graph theory was not accepted as mathematics by the mathematician for one century . which is the second research paper in graph theory , who is the author?. The word graph was used by Sylvester in 19th Century, what about Euler?
Euler didn't use the word graph. You can find his paper online, and this is a nice discussion of it: http://www.gss.ucsb.edu/Hopkins1.pdf
Borchardt's paper is the earliest that I know of. I don't think it discusses "graphs" but it does work with "trees" as an abstract concept. Hopefully you'll find something before 1860!
Feng , we know that there are many applied graph theory papers in IEEE proceedings . But we would like to know a brief history of graph theory after Euler.
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