Lesson plan
Graph enumeration
on 2, 3, and 4 labeled vertices: 2^{2-2}=1 tree with 2 vertices, 3^{3-2}=3 trees with 3 vertices, and 4^{4-2}=16 trees with 4 vertices. In combinatorics, an area of mathematics, graph enumeration describes a class of combinatorial enumeration problems in which one must count undirected or directed graphs of certain types, typically as a function of the number of vertices of the graph. These problems may be solved either exactly (as an algebraic enumeration problem) or asymptotically. The pioneers in this area of mathematics were George Pólya, Arthur Cayley and J. Howard Redfield.
Article summary
on 2, 3, and 4 labeled vertices: 2^{2-2}=1 tree with 2 vertices, 3^{3-2}=3 trees with 3 vertices, and 4^{4-2}=16 trees with 4 vertices. In combinatorics, an area of mathematics, graph enumeration describes a class of combinatorial enumeration problems in which one must count undirected or directed graphs of certain types, typically as a function of the number of vertices of the graph. These problems may be solved either exactly (as an algebraic enumeration problem) or asymptotically. The pioneers in this area of mathematics were George Pólya, Arthur Cayley and J. Howard Redfield.
Key claims
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Discussion questions
- Summarise the article in your own words. Which single claim would you verify first, and why?
- Which claim in this article is most likely to be revised as the sources update? How would you check its current status?
- If two sources disagreed about one of these facts, what would you need in order to trust one over the other?
Bibliography
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Key claims and bibliography are generated from the same tracked claims and sources as the article page.