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here we've got two graphs a graph G and a graph H are these two graphs the same does G equal H well certainly not because they have different vertices ABC X Y Z so they're not equal they also don't quite look the same the graph G is drawn to look like a path whereas the graph H is drawn more in the form of a bipartite graph however despite these differences we might take a close look at G and H and say that these two graphs have the same structure we could say look both graphs just consists of a single path of length 2 so in some way they are the same graph they have the same structure the term we use for this relationship between two graphs is isomorphic so we would say that the graph G is isomorphic to H and we could write it like this G is isomorphic to H and this is a symmetric relation we could also write the H is isomorphic to G you'll probably agree that this seems like a pretty fundamental and basic idea of graph theory one that we should definitely formalize and that's what we

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