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stephenmalina.com | ||
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www.jeremykun.com
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| | | | | For fixed integers $ r > 0$, and odd $ g$, a Moore graph is an $ r$-regular graph of girth $ g$ which has the minimum number of vertices $ n$ among all such graphs with the same regularity and girth. (Recall, A the girth of a graph is the length of its shortest cycle, and it's regular if all its vertices have the same degree) Problem (Hoffman-Singleton): Find a useful constraint on the relationship between $ n$ and $ r$ for Moore graphs of girth $ 5$ and degree $ r$. | |
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www.sirver.net
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nhigham.com
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| | | | | The trace of an $latex n\times n$ matrix is the sum of its diagonal elements: $latex \mathrm{trace}(A) = \sum_{i=1}^n a_{ii}$. The trace is linear, that is, $latex \mathrm{trace}(A+B) = \mathrm{trace}(A) + \mathrm{trace}(B)$, and $latex \mathrm{trace}(A) = \mathrm{trace}(A^T)$. A key fact is that the trace is also the sum of the eigenvalues. The proof is by... | |
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mln84.wordpress.com
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| | | The most common question students have about mathematics is "when will I ever use this?" Many math teachers would probably struggle to give a coherent answer, beyond being very good at following precise directions. They will say "critical thinking" but not much else concrete. Meanwhile, the same teachers must, with a straight face, tell their... | ||
