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Results tagged with combinatorial-designs
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user 4248
Design theory is the subfield of combinatorics concerning the existence and construction of highly symmetric arrangements. Finite projective planes, latin squares, and Steiner triple systems are examples of designs.
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Is there a 7-regular graph on 50 vertices with girth 5? What about 57-regular on 3250 vertices?
This is the Moore graph, which is a regular graph of degree $d$ with diameter $k$, with maximum possible nodes. A calculation shows that the number of nodes $n$ is at most
$$
1+d \sum_{i=0}^{k-1} (d- …
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