I am trying to use the nauty graph generator to count the number of non-isomorphic graphs with specified properties, but I am hindered by the fact that it seems nauty_geng only allows a fixed number of vertices.

For example, the following code counts the number of (non-isomorphic) connected graphs on 5 vertices:

```
count = 0
for g in graphs.nauty_geng("5 -c"):
count += 1
print count
```

The Sage output is: 21.

However, if I try to count the number of connected graphs on *n* vertices for *n* in a certain range, say *n*=3,4,5,6, as with the following code,

```
for n in range(3,7):
count = 0
for g in graphs.nauty_geng("n -c"):
count += 1
print (n,count)
```

,the count remains equal to zero for each *n*, and the situation is the same for all similar codes I have tried. The result is that in order to see what happens for multiple values of *n*, I must manually change all occurrences of *n* in the code.

Is this the meaning of "At a minimum, you must pass the number of vertices you desire," a statement in the help box?

Is there any way around this?

Thanks for any help with this!