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Stability of Cayley graphs on abelian groups of odd order

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 نشر من قبل Dave Witte Morris
 تاريخ النشر 2020
  مجال البحث
والبحث باللغة English
 تأليف Dave Witte Morris




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Let $X$ be a connected Cayley graph on an abelian group of odd order, such that no two distinct vertices of $X$ have exactly the same neighbours. We show that the direct product $X times K_2$ (also called the canonical double cover of $X$) has only the obvious automorphisms (namely, the ones that come from automorphisms of its factors $X$ and $K_2$). This means that $X$ is stable. The proof is short and elementary. The theory of direct products implies that $K_2$ can be replaced with members of a much more general family of connected graphs.



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