Graph isomorphism

Imagine you have two pictures of the exact same thing, but one picture might be flipped upside down or turned around. Graph isomorphism is like trying to figure out if these two pictures are actually the same thing or if they are different.

But instead of pictures, we're talking about graphs, which are just a bunch of dots (we call them vertices) and lines (we call them edges) connecting them. So, to check if two graphs are isomorphic (that just means they're the same thing in a different form), we have to make sure that each vertex in one graph corresponds to a vertex in the other graph. And we also have to make sure that the edges connecting those vertices are the same in both graphs.

It's a little bit like a puzzle, trying to fit all the pieces of one graph onto the other graph perfectly. And sometimes it can be easy to tell if two graphs are isomorphic, but other times it can be really tricky, especially if the graphs are very big or have lots of complicated connections between the vertices. That's why people study graph isomorphism - to come up with ways to figure out if two graphs are the same or not.