Strongly regular graph: Difference between revisions

Revision as of 15:41, 4 May 2022

Revision as of 15:41, 4 May 2022

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which must be integers.

In 1960, [[Alan Hoffman]] and [[Robert Singleton]] examined those expressions when applied on [[Moore graph]]s that have ''λ'' = 0 and ''μ'' = 1. Such graphs are free of triangles and quadrilaterals, hence have a girth of 5. Substituting the values of ''λ'' and ''μ'', it can be seen that <math>v = k^2 + 1</math>, and the multiplicities reduce to

:<math>M_{\pm} = \frac{1}{2}\left[k^2 \pm \frac{2k - k^2}{\sqrt{4k - 3}}\right]</math>