Graph isomorphism refers to the relationship between two graphs that can be transformed into each other by relabeling their vertices. This means that there exists a one-to-one correspondence between the vertex sets of the two graphs that preserves the adjacency relationship, meaning if two vertices are connected in one graph, their corresponding vertices in the other graph are also connected. Understanding graph isomorphism is crucial when analyzing the eigenvalues of graphs, as isomorphic graphs share the same spectrum of eigenvalues, which can reveal important structural properties.
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