Find an example of two non-isomorphic regular graphs $H_1$ and $H_2$ of same size and order satisfy these two conditions:
for all 2-element subsets $S_1 \subset V(H_1)$ and $S_2 \subset V(H_2)$, the graphs $H_1-S_1$ and $H_2 -S_2$ are not isomorphic; and
there exist 3-element subsets $T_1 \subset V(H-1)$ and $T_2 \subset V(H_2)$ such that $H_1 -T_1$ and $H_2 -T_2$ are isomorphic.
I have checked some pairs of 2-regular and 3-regular graphs of the same size and order, but can't find any examples that satisfy these 2 condition. I wonder if someone can give me a hint.