Homeomorphic Relation

See: Graph, Crossing Edge, Connected Graph, Planar Graph.

References

http://en.wikipedia.org/wiki/Homeomorphism_%28graph_theory%29
- In graph theory, two graphs [math]\displaystyle{ G }[/math] and [math]\displaystyle{ G' }[/math] are homeomorphic if there is an isomorphism from some subdivision of [math]\displaystyle{ G }[/math] to some subdivision of [math]\displaystyle{ G' }[/math]. 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.

(Winter, 2005a) ⇒ Dale Winter. (2005). “Planar Graphs." webpage accessed 2005-Aug-25
- QUOTE: Two graphs, G and H are defined to be homeomorphic if you can make one graph into the other by inserting vertices of degree 2.