Alternatively, notice that in \(G_1\text{,}\) the vertex \(a\) is adjacent to every other vertex. In \(G_2\text{,}\) there is also a vertex with this property: \(c\text{.}\) So build the bijection \(g:V_1 \to V_2\) by defining \(g(a) = c\) to start with. Next, where should we send \(b\text{?}\) In \(G_1\text{,}\) the vertex \(b\) is only adjacent to vertex \(a\text{.}\) There is exactly one vertex like this in \(G_2\text{,}\) namely \(d\text{.}\) So let \(g(b) = d\text{.}\) As for the last two, in this example, we have a free choice: let \(g(c) = b\) and \(g(d) = a\) (switching these would be fine as well).
in-context