. STANFORD UNIVERSITY SCHOOL OF MEDICINE
STANFORD MEDICAL CENTER
300 PASTEUR DRIVE, PALO ALTO, CALIFORNIA

DEPARTMENT OF GENETICS DAvenport 1-1200
: a Exe,
Prof. J. Lederberg, Director February 19, 1965 xt. 5052

Dr. Donald W. Grace
Procter & Gamble Co.
Ivorydale Technical Center
Cincinnati 17, Ohio

Dear Dr. Grace:

I am very sorry to have learned about your work on polyhedra only after
you left. Surprisingly enough, it has a distinct bearing on chemistry, as
I can perhaps best explain by referring immediately to the enclosures.

Especially as regards the note on Hamilton circuits, the extension to larger
grapns is of greater academic than practical concern. However ,having once gotten
started in this direction, I find it rather irritating not to have a deeper insight
than I do into the enumeration of these graphs generally. I am looking forward to
Professor Polya's return as a vrobable help. (He chose the wrong year to go away
or I nto work on such problems.)

I wanted to ask you whether you might be interested to continue your analysis
on some of these problems. For example, the exploration of the Hamilton circuits
in the range nj4- nig (i.e. n vertices) might. recheck the isomorphisms. Thus,
one might use the face-dissection program to generate only non-trigonal forms,
viz., by avoiding adjacent edges, and-using-oniy-non-trigenat-parents (I have to
strike that out since a trigonal parent can generate a non-trigonal offsoring::
needless to say, since one starts with the tetrahedron). Trigonal forms are
probably most efficiently generated as combinations of the ways that the vertices
of the lower order graphs can be marked for expansion into triangles. This can also
be turned into a test for isomorphism (via the Hamilton circuit of the reduced
figure, marked). As you will see, all the polyhedra in your main list (up ton 8)
do have Hamilton circuits provided the equisurroundness criterion holds through

Ny G°

another proposal might be check Tait's conjecture through Nog by using your
program through one more step, but saving only non-trigonal forms. This would
entail using the non-trigonal ny7g's and avoiding adjacent edses there; and also
the mono-trigonal nig's in just the fashion to enlarge the triangle. To go ton
may sé difficult but not impossible, as one would have to build all the mono-
trigonal nog's as well as the foregoing. But this can be done merely by marking
one vertex all possible ways on the nontrigonal nig's.

This is rather tiresome to have to deal with by letter. George Forsythe thought
it might be reasonable to ask you whether you had any interest in returning briefly
to Stanford at some convenient time that we might discuss these oroblems and perhaps

consider: some further runs.

“canwhile, I wonder if you can svare another. copy of your thesis, which is in
short supply here; also the reoroduction of the listings-is not all it could be.
If you shoula happen to have card-deck or tave storage of your output tables, it
micat be sspecially heloful.

Sincerely,

YD det ok
LT. J.P. KENNEDY, JR., LABORATORIES FOR MOLECULAR MEDICINE, DEDICATED TO RES ii IN MENTAL RETARDATION| —=—*
MOLECULAR BIOLOGY HEREDITY NEUROBIOLOGY * DEVELOPMENTAL/MEDICINE