202308231008

Type :Note Tags : Algebraic Graph Theory

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Regular Permutation Groups

Let $(\Gamma ,X)$ be a permutation group. $\Gamma$ is said to be Semiregular on $X$ if $\forall x\in X,{\Gamma }_x=\{1\}$. Which is to say that the only permutation that has an fixed point is the identity permutation. If $\Gamma$ is also transitive, then it is called regular.

In spirit, regular permutation groups mimic cycles.

The most common example of Regular permutation groups are cycles

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