Lesson plan
Integral graph
, is one of the only integral cycle graphs, whose adjacency matrix has eigenvalues 0, 0, 2, -2 . The red graph is not integral, as its eigenvalues are 0, -1, \frac{\sqrt{17} + 1}{2}, \frac{-\sqrt{17} + 1}{2} . In the mathematical field of graph theory, an integral graph is a graph whose adjacency matrix's spectrum consists entirely of integers. In other words, a graph is an integral graph if all of the roots of the characteristic polynomial of its adjacency matrix are integers. The notion was introduced in 1974 by Frank Harary and Allen Schwenk.
Article summary
, is one of the only integral cycle graphs, whose adjacency matrix has eigenvalues 0, 0, 2, -2 . The red graph is not integral, as its eigenvalues are 0, -1, \frac{\sqrt{17} + 1}{2}, \frac{-\sqrt{17} + 1}{2} . In the mathematical field of graph theory, an integral graph is a graph whose adjacency matrix's spectrum consists entirely of integers. In other words, a graph is an integral graph if all of the roots of the characteristic polynomial of its adjacency matrix are integers. The notion was introduced in 1974 by Frank Harary and Allen Schwenk.
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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.