Lesson plan
Two-graph
In mathematics, a two-graph is a set of unordered triples chosen from a finite vertex set X, such that every unordered quadruple from X contains an even number of triples of the two-graph. A regular two-graph has the property that every pair of vertices lies in the same number of triples of the two-graph. Two-graphs have been studied because of their connection with equiangular lines and, for regular two-graphs, strongly regular graphs, and also finite groups because many regular two-graphs have interesting automorphism groups. A two-graph is not a graph and should not be confused with other objects called 2-graphs in graph theory, such as 2-regular graphs.
Article summary
In mathematics, a two-graph is a set of unordered triples chosen from a finite vertex set X, such that every unordered quadruple from X contains an even number of triples of the two-graph. A regular two-graph has the property that every pair of vertices lies in the same number of triples of the two-graph. Two-graphs have been studied because of their connection with equiangular lines and, for regular two-graphs, strongly regular graphs, and also finite groups because many regular two-graphs have interesting automorphism groups. A two-graph is not a graph and should not be confused with other objects called 2-graphs in graph theory, such as 2-regular graphs.
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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.