isomorphic graph

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June 29, 2026

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Two graphs, G and H, are considered isomorphic if there's a one-to-one mapping between their vertices that preserves adjacency. This means that if two vertices are connected by an edge in graph G, their corresponding vertices in graph H must also be connected by an edge, and vice versa. Essentially, isomorphic graphs are structurally identical, even if their vertices are labeled differently. For example, a graph with vertices labeled 1, 2, 3, 4 and edges (1,2), (2,3), (3,4), (4,1) is isomorphic to a graph with vertices labeled A, B, C, D and edges (A,B), (B,C), (C,D), (D,A). Both represent a cycle of four vertices.1

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combinatorics
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…H are said to be isomorphic (written G ≃ H) if there exists a one–one correspondence between their vertex sets that preserves adjacency. For example, G₁ and G₂, shown in Figure 3, are isomorphic under the correspondence x_i ↔ y_i.
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…H are said to be isomorphic (written G ≃ H) if there exists a one–one correspondence between their vertex sets that preserves adjacency. For example, G₁ and G₂, shown in Figure 3, are isomorphic under the correspondence x_i ↔ y_i.
Read More