Determine all isomorphism classes of trees on six vertices how can I determine all isomomorphism classes of trees on six vertices?
 A: A tree on $6$ vertices has $5$ edges and each vertex has degree between $1$ and $5$, with the sum of degrees equal to $10$. Look at the degree sequences. There's $(5,1,1,1,1,1)$, $(4,2,1,1,1,1)$, $(3,3,1,1,1,1)$, $(3,2,2,1,1,1)$, and $(2,2,2,2,1,1)$.
For each sequence, can you figure out all the isomorphism classes with that degree sequence?
A: These can be computed using geng which comes with nauty.  The command is:
geng 6 5:5 -c

We set the parameters 6 vertices, between 5 and 5 edges, and -c for connected.  The above will output the graphs in a computer format.  If we redirect the output to a file:
geng 6 5:5 -c > temp.txt

we can then use showg to give the adjacency lists.  The command is:
showg temp.txt

which outputs
Graph 1, order 6.
  0 : 5;
  1 : 5;
  2 : 5;
  3 : 5;
  4 : 5;
  5 : 0 1 2 3 4;

Graph 2, order 6.
  0 : 4 5;
  1 : 5;
  2 : 5;
  3 : 5;
  4 : 0;
  5 : 0 1 2 3;

Graph 3, order 6.
  0 : 4 5;
  1 : 4;
  2 : 5;
  3 : 5;
  4 : 0 1;
  5 : 0 2 3;

Graph 4, order 6.
  0 : 4;
  1 : 4;
  2 : 5;
  3 : 5;
  4 : 0 1 5;
  5 : 2 3 4;

Graph 5, order 6.
  0 : 3 5;
  1 : 4 5;
  2 : 5;
  3 : 0;
  4 : 1;
  5 : 0 1 2;

Graph 6, order 6.
  0 : 3 5;
  1 : 4 5;
  2 : 4;
  3 : 0;
  4 : 1 2;
  5 : 0 1;

