[seqfan] Pictures of simple cubic graphs

Richard Mathar mathar at strw.leidenuniv.nl
Wed Feb 8 13:15:26 CET 2012

Vaguely related to http://oeis.org/A002851, I have created 3D "pictures"
of the simple cubic graphs in molfile and VRML97 format, and added the most
relevant of them as a JPG screen shot to
http://en.wikipedia.org/wiki/Table_of_simple_cubic_graphs .
This is merely a nice display of the structure of these, and does not
add anything that was not known before. The actual impetus was to
investigate what the symmetries of the associated Wigner 3j-symbols are
(that have been tabulated faithfully as it seems by Yutsis et al.).

If time permits, I may also add the associated automorphism group to the
wikipedia page. (I'll have to automate some interface to http://cs.anu.edu/au/~bdm/nauty )

This currently covers up to 12 vertices (more on request).
See http://www.strw.leidenuniv.nl/~mathar/progs/Ywrl.zip for the VRML97
files and http://arxiv.org/src/1109.2358v3/anc/ for the molfiles.
The molfiles have been generated by a Java program and then converted to VRML
with Jmol .

The strange file names inherit from an attempt to introduce unique file names.
The "Y" means "Yutsis" the Wxxx indicates the Wiener index, and the EExxxxx
indicates the first 7 digits of the Estrada Index without the decimal dot.
(Kirchhoff indices available on request.)


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