Isomorphism and Subgraphs · Medium problem

Let $G_1$ have vertices $1,\ldots,6$ and edges $12,23,34,45,56,16,14$ (a $6$-cycle plus the chord $14$ joining opposite vertices). Let $G_2$ have vertices $a,\ldots,f$ and edges $ab,bc,cd,de,ef,af,bd$ (a $6$-cycle plus the chord $bd$). Consider the map $\varphi$ sending $1,2,3,4,5,6$ to $a,b,c,d,e,f$ in order. How many of $G_1$'s $7$ edges map under $\varphi$ to a pair that is NOT an edge of $G_2$?