Let $G$ be a group and let $C$ be a subset of $G$ that is closed under taking inverses and does not contain the identity. Then the Cayley graph $X=Cay(G, C)$ is the graph with vertex set $G$ and edge set $$ E(Cay(G, C))=\{ gh \ | \ hg^{-1}\in C\}.$$ We say that $C$ is connection set.
Is there relationship between valency of Cayley graph $X$ and number of connection set $C$?