When are graphs the same?

A graph is fully defined by its vertex and edge sets.  However, the same graph can be drawn differently.  Different ways to represent the same graph are often considered immaterial.  This approach is captured by the definition of isomorphic graphs:

(Taken from the Graph Theory Module)

In other words, two graphs are isomorphic if there is a bijective mapping ƒ of vertices of G on the vertices of H such that if and only if .


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