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Let $X(G,S)$ be the (undirected) Cayley graph, with $G$ group and $S \subseteq G$ such that $1_G \notin S$ and $S=S^{-1}$. Is the complement of X$X$ a Cayley graph?

Let $X(G,S)$ be the (undirected) Cayley graph, with $G$ group and $S \subseteq G$ such that $1_G \notin S$ and $S=S^{-1}$. Is the complement of X a Cayley graph?

Let $X(G,S)$ be the (undirected) Cayley graph, with $G$ group and $S \subseteq G$ such that $1_G \notin S$ and $S=S^{-1}$. Is the complement of $X$ a Cayley graph?

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Complement of a Cayley graph

Let $X(G,S)$ be the (undirected) Cayley graph, with $G$ group and $S \subseteq G$ such that $1_G \notin S$ and $S=S^{-1}$. Is the complement of X a Cayley graph?