Subject: RE: funny question

From: Andrew Seniuk <[email-masked]>
Date: Tue, 17 Jan 1995 15:11:53 -0600

Dear Dr. Agrafiotis,

I am a Master's student in Theoretical Chemistry.  These are my suggestions,
which may be more-or-less fragmentary (I haven't formed them just yet).

   - if there is a 1-1 correspondence between valence electron pairs and edges,
     with a loop for a lone-pair, and multiple edges for general bonding, and
     if only a single "resonance structure" (hereafter unquoted) is considered
     to represent a molecule, then my hypotheses are established.
   - the total number of arcs in this graph is then easily established by the
     stoichiometry (and the molecular charge).  Unpaired electrons are not
     being treated here now, so no free radicals or odd-electron systems.
   - if the vertex set (distinguished by nuclear charge, lets suppose) is
     given (I mean we choose some fixed stoichiometry), then not only the
     number of edges, but moreover the DEGREE of each vertex is established
     simply - it should be the "valence" of the atom, eg) deg(H) = 1, deg(O) =
     deg(N) = deg(C) = 4, etc..
   - Note that the above includes lone pairs.  It is convenient that a loop
     (lone pair) contributes +2 to the degree of the vertex on which it
     resides, since then formal charge calculations, which offer other useful
     restrictions to guide us in the solution of this problem, are trivial.
     (Nuclear charge minus the vertice's degree.)
   - in fact, you are interested in the total number of connected graphs over
     some fixed stoichiometry, subject the the above constraints.
   - since different resonance structures of the same molecule will be
     ennumerated this way, and I see this as occurring in a subtle way, this
     approach may be frustrated.

I hope you will let me know if this is of some use for you.

Andy
[email-masked]