Strongly regular graph: Difference between revisions

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Revision as of 16:11, 24 May 2025

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* Absolute bound: <math>v \le \frac{f(f+3)}{2}</math> and <math>v \le \frac{g(g+3)}{2}</math>.

* Claw bound: if <math>r + 1 > \frac{s(s+1)(\mu+1)}{2}</math>, then <math>\mu = s^2</math> or <math>\mu = s(s+1)</math>.

If any of the above condition(s)conditions are violated for anya set of parameters, then there exists no strongly regular graph for those parameters. Brouwer has compiled such lists of existence or non-existence [https://www.win.tue.nl/~aeb/graphs/srg/srgtab.html here] with reasons for non-existence if any. For example, there exists no srg(28,9,0,4) because that violates one of the Krein conditions and one of the absolute bound conditions.

===The Hoffman–Singleton theorem===