Walks, Paths and Connectivity · Medium problem

A graph on vertices $1,\ldots,9$ consists of a $6$-cycle $1\text{-}2\text{-}3\text{-}4\text{-}5\text{-}6\text{-}1$ together with three pendant vertices: $7$ attached to $1$, $8$ attached to $3$, and $9$ attached to $5$. If vertex $1$ is deleted, what is the size of the largest resulting connected component?