# Strongly regular graph and Steiner system

For the complete graph $K_4$ as a strongly regular graph, what should he parameter $\mu$ be? Due to K4 is complete so it has no non-adjacent vertices, Mathworld gave its $\mu=0$,but is $\mu=2$ also allowed in such special case? http://mathworld.wolfram.com/TetrahedralGraph.html

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wouldn't that be any number since there's no non-adjacent vertices? – Keivan May 24 '12 at 1:25
I'd recommend including a definition of $\mu$ in the body of the question. – Gerry Myerson May 24 '12 at 1:31
Please post the second question separately. Questions can include subquestions that are aspects of the same problem, but asking two completely separate questions in one post makes search and tagging more difficult, mixes up answers to different things and forces people to read about both things when they're only interested in one of them. – joriki May 24 '12 at 5:47
Are you aware that you can edit your question? You posted the second part as a separate question (as I'd suggested) but failed to remove it here; that's potentially very wasteful as people providing answers to the two questions may not be aware of the effort already invested in the other version. I removed that part. – joriki May 25 '12 at 6:52

The entry "strongly regular parameters" in the MathWorld article you link to is slightly misleading, as it could be taken to imply that a strongly regular graph has a unique set of such parameters. If you take a careful look at the definition of strong regularity, you'll find there's nothing there that implies that a strongly regular graph can't be an $\operatorname{srg}(v,k,\lambda,\mu)$ for different values of $\mu$. For a complete graph, any value of $\mu$ will do. Note also that the Wikipedia article says that "some authors exclude graphs which satisfy the definition trivially, namely those graphs which are the disjoint union of one or more equal-sized complete graphs". Under this restricted definition, the set of parameters is indeed unique.