/sci/ - Science & Math

>>11701026
>what's wrong with my thinking?
Sometimes I can give clean, simple explanations for why something doesn't work.
In this case I can't. It literally just doesn't work.
The best I can do is some garbage like "Just because a map between graphs preserves degree doesn't mean it's an isomorphism."
>>11701154
There are all sorts of criteria, but I'm not a graph theorist, so I couldn't really give you any references.
For example, if we had an isomorphism between those two graphs from earlier, it would preserve vertex degree. So it sends the vertex with degree three to the other vertex with degree three.
Now, if we remove the degree three vertex from the graph on the left, we have three connected components, two with one vertex, one with three vertices.
If we remove the vertex with degree three from the other one, we have two connected components with two vertices, and a single connected component with one vertices.
However, an isomorphism of the entire graphs would induce an isomorphism of the two subgraphs, and thus bijections between the vertices of the connected components. But that's impossible.