Isomorphic graphs same structure from "summary" of Introduction to Graph Theory by Douglas Brent West
Two graphs that are isomorphic have the same structure, even if the vertices and edges are labeled differently. Formally, two graphs G and H are isomorphic if there is a bijection f from the vertices of G to the vertices of H such that uv is an edge of G if and only if f(u)f(v) is an edge of H. In other words, two graphs are isomorphic if they have the same number of vertices connected in the same way. Isomorphic graphs can be thought of as different ways of representing the same underlying structure. For example, consider two graphs that both have four vertices, where each vertex is connected to exactly three other vertices. These two graphs are isomorphic, even if the vertices are labeled differently or arranged in a different order. The key is that the connections between vertices are the same in both graphs. To determine if two gr...
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