Isomorphism and Subgraphs · Hard problem

Let $G$ have vertices $1,\ldots,6$ and edges $12,13,24,34,35,45,46$. Let $H$ have vertices $1,\ldots,6$ and edges $12,14,23,25,26,36,46$. These two graphs are isomorphic. Under the (unique) isomorphism $\varphi:G\to H$, vertex $4$ of $G$ is the only vertex of its degree in $G$. Find $\varphi(4)$.