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Necessary and sufficient conditions for the Cayley graph to be bipartite
Let $G$ be a finite group with identity $1$. If $S$ be an inverse closed generated subset of $G$, then $S$ is called a Cayley subset of $G$.The Cayley graph $\Gamma=\operatorname{Cay}(G, S)$ is a...
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The Cayley graph is bipartite if and only if there exists a homomorphism $\pi\colon G\to\mathbb Z/2\mathbb Z=\{0,1\}$ such that $\pi(S) \subseteq \{1\}$.If such a map exists, then the sets...
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