Figure S1 Subgraph counts, S(N,m), of each size, m, for straight chain alkanes up to length N = 12.
Figure S2 Subgraph counts, S(N,m), of each size, m, for monocyclic rings up to size N = 12.
Figure S3 Subgraph counts, S(N,m), of each size, m, for a selection of cages up to size N = 12.
Figure S4 Numbers of distinct moieties, M(N,m), of each size, m, for single oxygen-substituted chains of length N = 12 ordered by position of substitution.
Figure S5 Numbers of distinct moieties, M(N,m), of each size, m, for oxygen-substituted chains of length N = 12 ordered by position of substitution: none; 1 (alcohol), 1,2 (peroxide); 1,3; 1,4; and 1,5.
Figure S6 Numbers of distinct moieties, M(N,m), of each size, m, for straight chains up to 12 atoms with oxygen atoms substituted for the carbons in the terminal and 4th positions.
12
S(N,m)
12
S(N,m)
12
11 10 9 8
7 6 5 4 3 2 1 700
600
500
400
300 200
100 0
S(N,m)
m
0 100
200 300
400
500
600
700
800
icosahedrane
cuboctahedron adamantane
B8H8(--)
cubane
octahedrane
12 11 10 9 8 7 6 5 4 3 2 1
4
3
2
1
0
M(12,m)
Position
m
0
1 2
3 4
5
4
3
2
1
12 11 10 9 8 7 6 5 4 3 2 1
6
5
4
3
2
1
0
M(12,m)
Position
m
0
1 2
3
4 5
1-5
1-4
1-3
1-2
1
-12 11
10
9 8 7 6 5 4 3 2 1
4
3
2
1
0
M(N,m)
N
m
0 1
2
3 4
12
11 10
9 8
7
6
5
m
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15
a) S(N,m)
Glycine 5 4 4 3 1
Alanine 6 5 6 6 4 1
Cysteine 7 6 7 8 7 4 1
Serine 7 6 7 8 7 4 1
Proline 8 8 10 13 13 12 6 1
Threonine 8 7 9 11 12 10 5 1
Valine 8 7 9 11 12 10 5 1
Asparagine 9 8 10 11 12 12 10 5 1
Aspartic Acid 9 8 10 11 12 12 10 5 1
Isoleucine 9 8 10 13 15 15 11 5 1
Leucine 9 8 10 11 12 12 10 5 1
Methionine 9 8 9 10 10 9 7 4 1
Glutamic Acid 10 9 11 12 12 12 12 10 5 1
Glutamine 10 9 11 12 12 12 12 10 5 1
Lysine 10 9 10 11 11 10 9 7 4 1
Histidine 11 11 14 18 19 21 25 25 18 7 1
Arginine 12 11 13 14 14 13 12 12 12 10 5 1
Phenylalanine 12 12 15 19 24 26 30 34 32 22 8 1
