cographs

[Eric W. Weisstein]

---------- Forwarded message ----------
Date: Thu, 9 Oct 2003 15:22:25 -0500 (CDT)
From: Eric W. Weisstein <eric at weisstein.com>
To: GRAPHNET - Graph Theory <GRAPHNET at LISTSERV.NODAK.EDU>
Subject: Re: cographs

On Thu, 9 Oct 2003, Dr I. Sciriha wrote:

> Cographs, are the graphs belonging to the following recursively defined
> family:
> 1. K1 is a cograph,
> 2. If X is a cograph, then so is its complement, and
> 3. If X and Y are cographs, then so is their union XUY .
> Theorem: A graph is a cograph if and only if it does not have the path P_4
> as an induced subgraph.

I compute the counts of distinct cographs on n=1, 2, ... nodes as 
1,2,4,10,24,66,180,522, which looks identical to 
http://www.research.att.com/projects/OEIS?Anum=A000084
"Series-parallel networks with n unlabeled edges. Also called              
yoke-chains by Cayley and MacMahon."

Are these two sets of objects indeed isomorphic and, if so, is this known?

Cheers,
-Eric