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is any strongly regular graph a regular two-graph?

two-graph:a two graph is a collection $B$ of 3-subsets a set $X$ with the property that, for any 4-subset $Y$ of $X$, an even numbers of $B$ belong to $Y$.

regular two-graph:a two-graph is regular if it is a 2-design (with parameters $2-(n,3,\lambda)$ for some $\lambda$ )

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2 Answers 2

up vote 6 down vote accepted

No, there is a correspondence between certain strongly regular graphs and two-graphs but those strongly regular graphs have specific and restricted parameters.

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ok, that's right, if $\Gamma$ is strongly regular graph with parameters $(v,k,\lambda,\mu)$ then it's regular two-graph if and only if $k=2\mu$

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