Calculate all possible connected planar graphs with "E" edge
I'm developing a c++ program which calculate and draw all possible connected planar graphs with given E number edge. Like this :
My first thought was to find all possible solutions for the N edge by adding one edge to after finding the answer to (n-1) by doing recursion.
As you can see in the picture, the solution of the problem n = 4 is basically an improved version of the solution n = 3 with one edge more.
But it did not feel like a very effective solution. I could not find this problem in a particular algorithm.
is there any other way of finding and drawing all possible connected planar graphs with E edge?
is there any other way of finding and drawing all possible connected planar graphs with E edge?
Start with the complete graph K(E+1) - this will have (E+1) vertices and E(E+1)/2 edges. Enumerate the edges 1 .. E(E+1)/2.
- For each permutation of
Evalues from the set<1 .. E(E+1)/2>- Keep those
Eedges and delete the rest - Delete any unconnected vertices
- If the graph is connected, planar and is not isomorphic to a previous graph then
- It is a new unique graph with E edges.
- Keep those
You can probably perform significant optimisations by considering the symmetry of the complete graph and eliminating permutations that have a combination of rotational and/or reflectional symmetry with a previous permutation.
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