Subdivision (graph theory)

In graph theory, two graphs ${\displaystyle G}$ and ${\displaystyle G'}$ are homeomorphic if there is a graph isomorphism from some subdivision of ${\displaystyle G}$ to some subdivision of ${\displaystyle G'}$. If the edges of a graph are thought of as lines drawn from one vertex to another (as they are usually depicted in illustrations), then two graphs are homeomorphic to each other in the graph-theoretic sense precisely if they are homeomorphic in the sense in which the term is used in topology.

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