Hi and welcome to the Matladpi blog! In this post I will concentrate on the enumeration of homeomorphically irreducible trees, calculating the quantity of these for size v = 21. Here is a picture:
![](https://static.wixstatic.com/media/af42e7_e892071abad54fa0b5de745b305fcb5c~mv2_d_2322_4128_s_2.jpg/v1/fill/w_980,h_1742,al_c,q_85,usm_0.66_1.00_0.01,enc_auto/af42e7_e892071abad54fa0b5de745b305fcb5c~mv2_d_2322_4128_s_2.jpg)
So, first we evaluated the number of forms for branches of sizes 1 - 10 with the branch form generator (BFG). The size 11 case will be used in some later posts.
Next, we will enumerate h21 by using the algorithm BFG -> TGA, where TGA stands for tree generation algorithm.
Here are the pictures:
![](https://static.wixstatic.com/media/af42e7_733e0e12db204e78adbfaa82dea8ca5c~mv2_d_2322_4128_s_2.jpg/v1/fill/w_980,h_1742,al_c,q_85,usm_0.66_1.00_0.01,enc_auto/af42e7_733e0e12db204e78adbfaa82dea8ca5c~mv2_d_2322_4128_s_2.jpg)
![](https://static.wixstatic.com/media/af42e7_5929f0316c7b4ea68db7b1bb5fbe3ebb~mv2_d_2322_4128_s_2.jpg/v1/fill/w_980,h_1742,al_c,q_85,usm_0.66_1.00_0.01,enc_auto/af42e7_5929f0316c7b4ea68db7b1bb5fbe3ebb~mv2_d_2322_4128_s_2.jpg)
![](https://static.wixstatic.com/media/af42e7_bcefcf53d16d4ae58b684e1b0011fea7~mv2_d_2322_4128_s_2.jpg/v1/fill/w_980,h_1742,al_c,q_85,usm_0.66_1.00_0.01,enc_auto/af42e7_bcefcf53d16d4ae58b684e1b0011fea7~mv2_d_2322_4128_s_2.jpg)
So h21 = 5671. Njäf! said.
I am Jesse Sakari Hyttinen and I will see you in the next post!