[seqfan] Re: Counting multigraphs

[Richard Guy]

4 1-valent vertices, i.e., 2 disjoint edges.
3 1-valent vertices, i.e., i edge & a dijoint loop.
3 vertices, valences 1,2,1, i.e., a path of 2 edges.
12 is an edges with a loop at one end.
11 is two disjoint loops.
2 is one vertex with two loops
22 is two vertices with 2 parallel edges.    R.


On Mon, 20 Jun 2011, franktaw at netscape.net wrote:

> Sorry, I don't understand the representation scheme you are using here.
>
> Franklin T. Adams-Watters
>
> -----Original Message-----
> From: Richard Guy <rkg at cpsc.ucalgary.ca>
>
> Presumably 1111, 111, 121, 12, 11, 2 and 22.   R. 
>  
> On Mon, 20 Jun 2011, franktaw at netscape.net wrote: 
>  
>>  I don't understand A007717. I only count 5 multigraphs with 2 edges, 
> not 7: 2
>>  connected and 3 disconnected. The link in the sequence didn't get me 
> to
>>  anything useful. 
>>  
>>  Franklin T. Adams-Watters 
>>  
>>  -----Original Message----- 
>>  From: Charles Greathouse <charles.greathouse at case.edu> 
>>  
>>  A sequence defined in terms of A007717 was recently submitted, and an 
>>  editor asked if it and A007717 could be extended.  A007717 itself is 
>>  marked as an easy sequence, but I must admit that I'm not sure how to 
>>  extend it.  If it is easy, would someone add a program and more terms 
>>  (ideally a 10,000-term b-file, but the standard three lines would do 
>>  as well)?  I assume this is one of the things that is "well-known to 
>>  those who well-know it". 
>>  
>>  On the other hand, if it's not easy the keyword, at least, should be 
>>  removed (and whatever can be added should be). 
>>  
>>  Charles Greathouse 
>>  Analyst/Programmer 
>>  Case Western Reserve University 
>>  
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