Two graphs G and H are said to be homeomorphic if there is an Isomorphism from some subdivision of G to some subdivision of H. A subdivision of a Graph is obtained by adding vertices in the middle of existing edges.

**Homomorphism and****Homeomorphism are different**. Homomorphism is discussed in the previous post. If you have any doubt refer that post.**Figure Given Below Shows Graphs N, O and P which are Subdivisions of Graph M**

**Two graphs are homeomorphic if and only if they have at least one common subdivision.**

**The Two Graphs Shown Below are Homeomorphic to each other**

**The Common Subdivision of the Two Graphs is Shown Below**

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