# These are all the blocks ( = 2-connected graphs) with <= 11 edges,
# sorted by number of vertices and edges.
# Useful for testing whether the spanning tree generating function
# of a graph is completely reducible.

gr[3,3]:=[{{1,2},{1,3},{2,3}}]:

gr[4,4]:=[{{1,4},{1,3},{2,3},{2,4}}]:

gr[4,5]:=[{{1,4},{3,4},{1,3},{2,3},{2,4}}]:

gr[5,5]:=[{{3,5},{4,5},{1,2},{1,3},{2,4}}]:

gr[4,6]:=[{{1,4},{1,2},{3,4},{1,3},{2,3},{2,4}}]:

gr[5,6]:=[{{1,4},{1,5},{2,5},{1,3},{2,3},{2,4}},
{{1,4},{1,5},{2,5},{1,2},{3,4},{2,3}}]:

gr[6,6]:=[{{3,5},{1,2},{1,3},{2,4},{4,6},{5,6}}]:

gr[5,7]:=[{{1,4},{1,5},{2,5},{3,5},{4,5},
{3,4},{2,4}},{{1,4},{1,5},{2,5},{3,5},{4,5},{1,2},{2,3}},
{{1,4},{1,5},{2,5},{3,4},{1,3},{2,3},{2,4}}]:

gr[6,7]:=[{{2,5},{4,5},{1,2},{1,3},{3,6},{4,6},{5,6}},{{1,
5},{3,5},{4,5},{1,2},{2,6},{3,6},{4,6}},{{1,5},{3,5},{1,2},{
3,4},{2,6},{4,6},{5,6}}]:

gr[7,7]:=[{{3,5},{1,2},{1,3},{2,4},{4,6},{5,7},{6,7}}]:

gr[5,8]:=[{{1,4},{1,5},{2,5},{3,5},{4,5},{1,3},{2,3}
,{2,4}},{{1,4},{1,5},{2,5},{3,5},{4,5},{1,2},{3,4},{2,4}}]:

gr[6,8]:=[{{1,4},{1,5},{2,5},{3,4},{1,6},{2
,6},{1,3},{2,3}},{{1,5},{3,5},{1,2},{3,4},{1,6},{2,6},{1,3}
,{2,4}},{{1,4},{1,5},{3,5},{3,4},{1,6},{2,6},{2,3},{2,4}},{{
1,4},{1,5},{2,5},{1,2},{3,4},{1,6},{2,6},{2,3}},{{1,4},{2,5}
,{3,4},{1,6},{1,3},{2,3},{2,4},{5,6}},{{1,4},{2,5},{4,5},{1
,6},{1,3},{2,3},{2,4},{3,6}},{{1,4},{1,5},{2,5},{1,6},{2,6}
,{1,3},{2,3},{2,4}},{{1,4},{3,5},{4,5},{1,6},{2,6},{1,3},{2
,3},{2,4}},{{1,5},{4,5},{1,2},{3,4},{1,6},{2,6},{1,3},{2,3}}]:

gr[7,8]:=[{{4,5},{1,2},{2,6},{3,7},{1,3},{4,6},{5,7},{6,7}},{{1,
2},{3,4},{1,6},{4,7},{3,6},{5,6},{2,7},{5,7}},{{1,2},{2,6},{
3,7},{4,7},{1,3},{4,6},{5,6},{5,7}},{{1,2},{4,7},{1,3},{2,4}
,{3,6},{5,6},{5,7},{6,7}}]:

gr[8,8]:=[{{3,5},{6,8},{7,8},{1,2},{1,3},{2,4},{4,6},{5,7}}]:

gr[5,9]:=[{{1,4},{1,5},{2,5},{3,5},{4,5},{3,4},{1,3},{2,3},{2,4}}]:

gr[6,9]:=[{{1,4},{1,5},{2,5},{3,5},{3,4},{1,6},{2,6}
,{2,4},{3,6}},{{1,4},{1,5},{2,5},{4,5},{3,4},{1,6},{2,6},{2
,3},{3,6}},{{1,5},{2,5},{3,5},{4,5},{1,6},{2,6},{3,6},{4,6}
,{5,6}},{{1,4},{1,5},{2,5},{3,4},{1,6},{2,6},{1,3},{2,3},{2
,4}},{{1,4},{1,5},{2,5},{4,5},{1,2},{3,4},{2,6},{1,3},{3,6}}
,{{1,4},{1,5},{3,5},{1,2},{3,4},{1,6},{2,6},{2,3},{2,4}},{{1
,4},{3,5},{4,5},{1,2},{1,6},{2,6},{1,3},{2,3},{2,4}},{{1,4}
,{2,5},{4,5},{1,2},{1,6},{1,3},{2,3},{2,4},{3,6}},{{1,4},{1
,5},{1,2},{1,6},{2,6},{2,3},{3,6},{4,6},{5,6}},{{1,4},{2,5}
,{1,2},{3,4},{1,6},{1,3},{2,3},{2,4},{5,6}},{{1,5},{1,6},{2
,6},{1,3},{2,3},{2,4},{3,6},{4,6},{5,6}},{{1,4},{1,5},{3,5}
,{4,5},{1,2},{3,4},{1,6},{2,6},{2,3}},{{1,5},{3,5},{1,2},{3
,4},{1,6},{2,6},{1,3},{2,3},{2,4}},{{1,4},{1,5},{2,5},{3,5}
,{3,4},{1,6},{2,6},{1,3},{2,4}}]:

gr[7,9]:=[
{{3,5},{1,2},{4,7},{1,3},{2,4},{4,6},{5,6},{5,7},{6,7}},{{1,
4},{1,5},{3,5},{2,6},{4,7},{2,4},{3,6},{5,7},{6,7}},{{1,4},{
1,5},{3,5},{2,6},{3,7},{4,7},{2,4},{5,6},{6,7}},{{1,4},{1,5}
,{3,4},{2,6},{3,7},{2,4},{5,6},{5,7},{6,7}},{{1,4},{1,5},{3
,5},{2,6},{3,7},{2,4},{4,6},{5,7},{6,7}},{{1,4},{2,5},{4,5}
,{1,2},{3,7},{3,6},{4,6},{5,7},{6,7}},{{1,4},{2,5},{1,2},{3
,4},{4,7},{3,6},{5,6},{5,7},{6,7}},{{1,4},{1,5},{2,5},{3,7}
,{2,4},{3,6},{4,6},{5,7},{6,7}},{{1,4},{2,5},{1,2},{3,7},{4
,7},{3,6},{4,6},{5,6},{5,7}},{{1,5},{2,5},{3,5},{1,6},{3,7}
,{4,7},{4,6},{2,7},{6,7}},{{1,5},{2,6},{3,7},{4,7},{1,3},{2
,4},{5,6},{5,7},{6,7}},{{1,5},{3,5},{1,2},{2,6},{3,7},{4,7}
,{4,6},{5,7},{6,7}},{{1,5},{2,5},{3,7},{4,7},{3,6},{4,6},{5
,6},{1,7},{2,7}},{{3,5},{4,5},{1,2},{1,6},{3,7},{4,7},{5,6}
,{2,7},{6,7}},{{2,5},{1,2},{3,7},{4,7},{1,3},{4,6},{5,6},{5
,7},{6,7}},{{1,5},{2,5},{2,6},{3,7},{4,7},{1,3},{4,6},{5,7}
,{6,7}},{{1,2},{2,6},{3,7},{4,7},{1,3},{4,6},{5,6},{5,7},{6
,7}},{{1,2},{3,4},{1,6},{4,7},{3,6},{5,6},{2,7},{5,7},{6,7}}
,{{1,2},{1,6},{3,7},{4,7},{3,6},{4,6},{5,6},{2,7},{5,7}},{{1
,5},{3,5},{1,2},{3,7},{4,7},{4,6},{5,6},{2,7},{6,7}}]:

gr[8,9]:=[{{1,4},{2,5},{6,8},{7,8
},{2,6},{3,7},{1,3},{5,7},{4,8}},{{4,5},{6,8},{1,2},{4,7},{1
,3},{2,7},{6,7},{3,8},{5,8}},{{3,5},{6,8},{1,2},{3,7},{4,7}
,{2,8},{4,6},{1,7},{5,8}},{{6,8},{7,8},{1,2},{3,7},{1,3},{2
,4},{5,6},{5,7},{4,8}},{{6,8},{1,2},{3,7},{1,3},{2,4},{5,7}
,{6,7},{4,8},{5,8}},{{3,5},{6,8},{7,8},{1,2},{4,7},{1,3},{2
,4},{6,7},{5,8}}]:

gr[9,9]:=[{{3,5},{6,8},{1,2},{1,3},{2,4},{4,6},{5,7},{7,9},{8,9}}]:

gr[5,10]:=[{{1,4},{1,5},{2,5},{3,5},{4,5},{1,2},{3,4},{1,3},
{2,3},{2,4}}]:

gr[6,10]:=[{{1,4},{1,5},{2,5},{4,5},{1,2}
,{3,4},{1,6},{2,6},{2,3},{3,6}},{{1,4},{1,5},{2,5},{4,5},{1
,6},{2,6},{1,3},{2,3},{2,4},{3,6}},{{1,4},{1,5},{2,5},{3,4}
,{1,6},{2,6},{2,3},{3,6},{4,6},{5,6}},{{1,4},{1,5},{2,5},{3
,5},{1,2},{3,4},{1,6},{2,6},{2,4},{3,6}},{{1,5},{1,2},{1,6}
,{2,6},{1,3},{2,3},{2,4},{3,6},{4,6},{5,6}},{{1,4},{1,5},{1
,6},{2,6},{1,3},{2,3},{2,4},{3,6},{4,6},{5,6}},{{1,5},{2,5}
,{3,5},{4,5},{1,2},{1,6},{2,6},{3,6},{4,6},{5,6}},{{1,4},{2
,5},{1,2},{3,4},{1,6},{2,6},{1,3},{3,6},{4,6},{5,6}},{{1,4}
,{3,5},{4,5},{1,2},{3,4},{1,6},{2,6},{1,3},{2,3},{2,4}},{{1
,5},{2,5},{3,5},{1,2},{3,4},{1,6},{1,3},{2,3},{2,4},{4,6}},
{{1,4},{1,5},{2,5},{3,5},{3,4},{1,6},{2,6},{1,3},{2,3},{2,4}
},{{1,5},{3,5},{4,5},{1,2},{3,4},{1,6},{2,6},{1,3},{2,3},{2
,4}}]:

gr[7,10]:=[{{3,5},{1,2},{4,7},{1,3},{2,3
},{2,4},{4,6},{5,6},{5,7},{6,7}},{{2,5},{1,2},{3,4},{4,7},{1
,3},{2,4},{3,6},{5,6},{5,7},{6,7}},{{2,5},{4,5},{1,2},{3,7}
,{1,3},{2,4},{3,6},{4,6},{5,7},{6,7}},{{2,5},{1,2},{3,7},{4
,7},{1,3},{2,4},{3,6},{4,6},{5,6},{5,7}},{{2,5},{4,5},{3,4}
,{1,3},{3,6},{4,6},{1,7},{2,7},{5,7},{6,7}},{{1,5},{2,5},{3
,5},{1,6},{2,6},{3,7},{4,7},{4,6},{5,7},{6,7}},{{1,4},{2,5}
,{4,5},{1,6},{2,6},{3,7},{4,7},{3,6},{5,7},{6,7}},{{1,4},{4
,5},{1,2},{2,6},{3,7},{4,7},{3,6},{5,6},{5,7},{6,7}},{{1,4}
,{1,5},{3,4},{4,7},{2,3},{3,6},{5,6},{2,7},{5,7},{6,7}},{{1
,4},{3,5},{4,7},{1,3},{2,3},{4,6},{5,6},{2,7},{5,7},{6,7}},
{{3,5},{4,5},{1,3},{2,4},{3,6},{4,6},{1,7},{2,7},{5,7},{6,7}
},{{4,5},{1,2},{3,4},{1,6},{4,7},{3,6},{5,6},{2,7},{5,7},{6
,7}},{{1,4},{2,5},{4,5},{1,6},{3,7},{3,6},{4,6},{2,7},{5,7}
,{6,7}},{{4,5},{1,2},{1,6},{3,7},{4,7},{3,6},{4,6},{5,6},{2
,7},{5,7}},{{1,4},{1,5},{3,5},{3,4},{2,6},{4,7},{3,6},{2,7}
,{5,7},{6,7}},{{1,4},{1,5},{2,6},{3,7},{4,7},{2,4},{3,6},{5
,6},{5,7},{6,7}},{{1,4},{2,5},{3,4},{1,6},{2,6},{3,7},{4,7}
,{5,6},{5,7},{6,7}},{{1,4},{1,5},{4,5},{2,6},{3,7},{3,6},{4
,6},{2,7},{5,7},{6,7}},{{3,5},{1,2},{3,4},{4,7},{1,3},{4,6}
,{5,6},{2,7},{5,7},{6,7}},{{1,4},{3,5},{4,7},{1,3},{2,4},{3
,6},{5,6},{2,7},{5,7},{6,7}},{{1,4},{2,5},{4,5},{1,6},{3,7}
,{4,7},{3,6},{5,6},{2,7},{6,7}},{{1,4},{3,5},{1,6},{2,6},{3
,7},{4,7},{2,4},{5,6},{5,7},{6,7}},{{1,4},{4,5},{1,6},{3,7}
,{2,4},{3,6},{5,6},{2,7},{5,7},{6,7}},{{1,5},{3,5},{1,2},{2
,6},{3,7},{4,7},{4,6},{5,6},{5,7},{6,7}},{{1,5},{3,4},{4,7}
,{1,3},{2,4},{3,6},{5,6},{2,7},{5,7},{6,7}},{{1,4},{1,5},{2
,6},{3,7},{4,7},{2,3},{4,6},{5,6},{5,7},{6,7}},{{4,5},{1,2}
,{2,6},{3,7},{4,7},{1,3},{4,6},{5,6},{5,7},{6,7}},{{1,4},{4
,5},{1,6},{2,6},{3,7},{4,7},{3,6},{5,6},{2,7},{5,7}},{{1,4}
,{2,5},{3,4},{4,7},{1,3},{3,6},{5,6},{2,7},{5,7},{6,7}},{{1
,4},{3,5},{1,2},{3,4},{4,7},{3,6},{5,6},{2,7},{5,7},{6,7}},
{{1,4},{1,5},{2,6},{3,7},{4,7},{3,6},{4,6},{5,6},{2,7},{5,7}
},{{1,4},{2,5},{1,6},{3,7},{4,7},{3,6},{4,6},{5,6},{2,7},{5
,7}},{{3,5},{3,4},{1,3},{2,4},{4,6},{5,6},{1,7},{2,7},{5,7}
,{6,7}},{{4,5},{3,4},{1,3},{2,3},{4,6},{5,6},{1,7},{2,7},{5
,7},{6,7}},{{3,5},{1,2},{3,7},{4,7},{1,3},{2,4},{4,6},{5,6}
,{5,7},{6,7}},{{1,4},{3,5},{1,2},{2,6},{3,7},{4,7},{4,6},{5
,6},{5,7},{6,7}},{{1,4},{2,5},{1,2},{3,7},{4,7},{3,6},{4,6}
,{5,6},{5,7},{6,7}},{{1,4},{2,5},{3,7},{4,7},{1,3},{2,3},{4
,6},{5,6},{5,7},{6,7}},{{1,4},{2,5},{3,5},{2,6},{3,7},{4,7}
,{1,3},{4,6},{5,7},{6,7}},{{1,6},{2,6},{3,7},{4,7},{3,6},{4
,6},{5,6},{1,7},{2,7},{5,7}},{{1,5},{2,6},{3,7},{4,7},{3,6}
,{4,6},{5,6},{1,7},{2,7},{5,7}},{{1,4},{1,5},{3,7},{4,7},{2
,4},{3,6},{5,6},{2,7},{5,7},{6,7}},{{1,2},{1,6},{3,7},{4,7}
,{3,6},{4,6},{5,6},{2,7},{5,7},{6,7}},{{1,4},{3,5},{1,2},{3
,7},{4,7},{4,6},{5,6},{2,7},{5,7},{6,7}},{{1,4},{2,5},{4,5}
,{3,7},{3,6},{4,6},{1,7},{2,7},{5,7},{6,7}},{{1,5},{2,5},{3
,7},{4,7},{3,6},{4,6},{5,6},{1,7},{2,7},{6,7}},{{1,4},{3,5}
,{3,7},{2,4},{4,6},{5,6},{1,7},{2,7},{5,7},{6,7}},{{1,5},{2
,5},{1,6},{3,7},{4,7},{3,6},{4,6},{2,7},{5,7},{6,7}},{{1,5}
,{1,2},{3,7},{4,7},{3,6},{4,6},{5,6},{2,7},{5,7},{6,7}},{{3
,5},{1,2},{1,6},{3,7},{4,7},{4,6},{5,6},{2,7},{5,7},{6,7}}]:

gr[8,10]:=[{{1,5},{2,5},{6,8},{7,8},{4,7},{1,3}
,{2,4},{3,6},{6,7},{5,8}},{{1,5},{6,8},{7,8},{1,2},{3,4},{2
,6},{3,7},{5,6},{5,7},{4,8}},{{1,5},{3,5},{6,8},{7,8},{1,2}
,{3,6},{4,6},{2,7},{5,7},{4,8}},{{2,5},{4,5},{6,8},{7,8},{1
,2},{4,7},{1,3},{3,6},{6,7},{5,8}},{{1,5},{3,5},{4,5},{6,8}
,{7,8},{1,2},{2,6},{3,7},{6,7},{4,8}},{{1,5},{3,5},{6,8},{7
,8},{1,2},{2,6},{3,7},{4,7},{4,6},{5,8}},{{1,5},{3,5},{6,8}
,{7,8},{1,2},{2,6},{4,7},{4,6},{5,7},{3,8}},{{2,5},{6,8},{7
,8},{1,2},{4,7},{1,3},{3,6},{5,6},{5,7},{4,8}},{{1,5},{3,5}
,{7,8},{1,2},{3,6},{4,6},{2,7},{6,7},{4,8},{5,8}},{{3,5},{4
,5},{6,8},{7,8},{1,2},{2,8},{3,6},{4,6},{1,7},{5,7}},{{1,5}
,{3,5},{6,8},{7,8},{1,2},{2,6},{4,7},{3,6},{5,7},{4,8}},{{1
,5},{6,8},{7,8},{1,2},{3,4},{4,7},{2,8},{3,6},{5,6},{5,7}},
{{1,5},{2,5},{7,8},{1,6},{4,7},{3,6},{5,6},{2,7},{3,8},{4,8}
},{{1,5},{2,5},{1,6},{4,7},{3,6},{2,7},{6,7},{3,8},{4,8},{5
,8}},{{2,5},{6,8},{1,2},{4,7},{1,3},{3,6},{5,7},{6,7},{4,8}
,{5,8}},{{3,5},{6,8},{7,8},{1,2},{1,3},{2,4},{4,6},{5,7},{6
,7},{5,8}},{{1,5},{2,5},{3,5},{6,8},{7,8},{1,6},{2,6},{3,7}
,{4,7},{4,8}},{{1,5},{2,5},{6,8},{1,6},{2,6},{3,7},{4,7},{5
,7},{3,8},{4,8}},{{1,5},{3,5},{6,8},{7,8},{1,2},{2,6},{3,7}
,{4,6},{5,7},{4,8}},{{1,5},{2,5},{4,5},{6,8},{7,8},{1,6},{3
,7},{3,6},{2,7},{4,8}},{{1,4},{3,5},{6,8},{7,8},{1,2},{2,6}
,{3,7},{6,7},{4,8},{5,8}},{{1,4},{2,5},{6,8},{7,8},{1,6},{3
,7},{3,6},{2,7},{4,8},{5,8}},{{1,4},{6,8},{7,8},{1,2},{2,6}
,{3,7},{3,6},{5,7},{4,8},{5,8}},{{6,8},{7,8},{1,2},{3,4},{1
,6},{3,6},{2,7},{5,7},{4,8},{5,8}},{{1,6},{2,6},{4,7},{2,8}
,{3,6},{1,7},{5,7},{3,8},{4,8},{5,8}},{{7,8},{1,6},{2,6},{1
,3},{4,6},{2,7},{5,7},{3,8},{4,8},{5,8}},{{7,8},{1,6},{1,3}
,{2,4},{5,6},{2,7},{6,7},{3,8},{4,8},{5,8}},{{7,8},{1,2},{2
,6},{1,3},{4,6},{5,7},{6,7},{3,8},{4,8},{5,8}},{{4,5},{6,8}
,{7,8},{1,2},{4,7},{1,3},{2,7},{6,7},{3,8},{5,8}},{{6,8},{1
,2},{4,7},{1,3},{2,7},{5,7},{6,7},{3,8},{4,8},{5,8}},{{6,8}
,{1,2},{3,4},{3,7},{2,8},{1,7},{5,7},{6,7},{4,8},{5,8}},{{7
,8},{1,6},{2,6},{1,3},{2,4},{5,7},{6,7},{3,8},{4,8},{5,8}},
{{3,5},{6,8},{7,8},{1,2},{3,7},{4,7},{2,8},{4,6},{1,7},{5,8}
},{{6,8},{7,8},{1,2},{3,7},{1,3},{2,4},{5,7},{6,7},{4,8},{5
,8}},{{7,8},{1,2},{1,3},{4,6},{5,6},{2,7},{6,7},{3,8},{4,8}
,{5,8}},{{1,2},{1,6},{4,7},{2,8},{3,6},{5,7},{6,7},{3,8},{4
,8},{5,8}},{{7,8},{1,2},{1,6},{3,6},{4,6},{2,7},{5,7},{3,8}
,{4,8},{5,8}},{{7,8},{2,6},{1,3},{4,6},{5,6},{1,7},{2,7},{3
,8},{4,8},{5,8}},{{6,8},{7,8},{1,2},{1,3},{2,4},{3,6},{5,7}
,{6,7},{4,8},{5,8}},{{6,8},{7,8},{1,2},{2,6},{3,7},{1,3},{4
,6},{5,7},{4,8},{5,8}}]:

gr[9,10]:=[{{3,5},{7,8},{1,2},{1,3},{2,4},{4,6},{5,8},{6,9},
{7,9},{8,9}},{{3,5},{6,8},{1,2},{1,3},{2,4},{6,7},{4,8},{5,9
},{7,9},{8,9}},{{7,8},{1,2},{1,3},{2,4},{5,6},{3,8},{5,8},{4
,9},{6,9},{7,9}},{{1,4},{2,5},{6,8},{1,2},{3,7},{3,6},{4,8}
,{5,9},{7,9},{8,9}},{{1,4},{2,5},{7,8},{2,6},{1,3},{3,8},{5
,8},{4,9},{6,9},{7,9}},{{1,2},{2,8},{1,3},{4,6},{5,7},{4,8}
,{5,8},{6,9},{3,9},{7,9}},{{3,5},{6,8},{7,8},{1,2},{1,3},{2
,4},{4,8},{5,9},{6,9},{7,9}}]:

gr[10,10]:=[{{4,5},{7,8},{1,2},{3,4},{2,3},{5,6},{1,10},
{9,10},{6,7},{8,9}}]:

gr[6,11]:=[{{5,6},{1,6},{2,6},{3,5},{4,5},{1,2},{1,
4},{2,4},{3,4},{1,3},{2,3}},{{5,6},{1,6},{2,6},{3,6},{4,6},{
1,5},{2,5},{1,4},{2,4},{1,3},{2,3}},{{5,6},{1,6},{2,6},{3,6}
,{4,6},{1,5},{2,5},{1,2},{1,4},{3,4},{2,3}},{{5,6},{1,6},{2
,6},{3,6},{4,6},{1,5},{2,5},{3,5},{4,5},{1,4},{2,3}},{{1,6}
,{2,6},{3,6},{1,5},{2,5},{4,5},{1,4},{2,4},{3,4},{1,3},{2,3
}},{{5,6},{1,6},{2,6},{3,6},{4,6},{1,5},{1,2},{2,4},{3,4},{1
,3},{2,3}},{{5,6},{1,6},{2,6},{3,6},{4,6},{1,5},{2,5},{3,5}
,{4,5},{1,2},{1,3}},{{1,6},{2,6},{1,5},{2,5},{3,5},{4,5},{1
,4},{2,4},{3,4},{1,3},{2,3}}]:

gr[7,11]:=[{{1,6},{2,6},{4,6},{1,5},{3,5},{4,5},{1,4},{2,3
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{{2,6},{4,6},{1,5},{2,5},{3,5},{1,2},{1,4},{2,4},{1,3},{1,7}
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{{1,6},{3,6},{1,5},{2,5},{4,5},{2,4},{3,4},{1,3},{2,3},{1,7}
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{{7,8},{5,6},{1,6},{2,5},{4,5},{1,4},{3,7},{4,7},{2,8},{3,8}
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