Homeomorphism (graph theory)

<p>In <a href="/facts/Graph_theory/VVPCd4TX">graph theory</a>, two <a href="/facts/Graph_(discrete_mathematics)/kw3eIBUe">graphs</a> 
  
    
      
        G
      
    
    {\displaystyle G}
  
 and 
  
    
      
        
          G
          ′
        
      
    
    {\displaystyle G'}
  
 are homeomorphic if there is a <a href="/facts/Graph_isomorphism/SBjVIhwW">graph isomorphism</a> from some subdivision of 
  
    
      
        G
      
    
    {\displaystyle G}
  
 to some subdivision of 
  
    
      
        
          G
          ′
        
      
    
    {\displaystyle G'}
  
.  If the edges of a graph are thought of as lines drawn from one <a href="/facts/Vertex_(graph_theory)/WhlWmL3o">vertex</a> to another (as they are usually depicted in diagrams), then two graphs are homeomorphic to each other in the graph-theoretic sense precisely if their diagrams are <a href="/facts/Homeomorphism/jMfWg3Mn">homeomorphic</a> in the <a href="/facts/Topology/2EqW47cU">topological</a> sense.
</p>

Homeomorphism (graph theory) open-in-new

Homeomorphism (graph theory)