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Homomorphism
Two graphs G1 and G2 are said to be homomorphic, if each of these graphs can be obtained from the same graph 'G' by dividing some edges of G with more vertices. Take a look at the following example −
Divide the edge 'rs' into two edges by adding one vertex.
The graphs shown below are homomorphic to the first graph.
If G1 is isomorphic to G2, then G is homeomorphic to G2 but the converse need not be true.
Any graph with 4 or less vertices is planar.
Any graph with 8 or less edges is planar.
A complete graph Kn is planar if and only if n ≤ 4.
The complete bipartite graph Km, n is planar if and only if m ≤ 2 or n ≤ 2.
A simple non-planar graph with minimum number of vertices is the complete graph K5.
The simple non-planar graph with minimum number of edges is K3, 3.
Polyhedral graph
A simple connected planar graph is called a polyhedral graph if the degree of each vertex is ≥ 3, i.e., deg(V) ≥ 3 ∀ V ∊ G.
- 3|V| ≤ 2|E|
- 3|R| ≤ 2|E|