Question 58
For a graph $G$, let $G-\{x\}$ mean deleting vertex $x$ and all incident edges. Graphs $G,H$ both have vertices numbered $1,\ldots,n$, where $n\ge4$. Suppose $G-\{i\}-\{j\}$ and $H-\{i\}-\{j\}$ are isomorphic for every $1\le i\lt j\le n$. Prove $G,H$ are isomorphic.