Inspired by the thesis of Marleen van der Veen
on "pi-Logic" we wrote:
W.H. Hesselink, J.C. Hummelen, H.T. Jonkman, H.G. Reker, G.R. Renardel de Lavalette, M.H. van der Veen: Kekulé Cells for Molecular Computation, 18 April 2007 (24 pages).
The results up to Theorem 3 have been verified with the proof assistant PVS, see Reker's page.
This material was reworked and extended in May-June 2011. I took
a more liberal position than in the arxiv paper: the ports no longer
need to have degree 1; they are marked vertices instead. This led to
a paper that was submitted to Indagationes. An anonymous referee
pointed out that my objects of study were linkable
Delta-matroids in the sense of A. Bouchet. This resulted in the
W.H. Hesselink: Graph Theory for Alternating Hydrocarbons with Attached Ports, Indagationes Mathematicae 24 (2013) 115-141.
The work has also resulted in the classification of the linkable cells of rank 6, with in almost all cases corresponding graphs. The details are contained in the archive kekprog, which contains data files, C-programs, and a corresponding makefile. Under unix/linux, it can be opened by the call 'tar zxvf kekprog.tgz'. It then makes a directory 'cprog', with the files as announced. All files are plain text files that can be read and modified by means of a simple text editor. Consult the file README included.
Comments and questions are welcome.
Back to my home page.
Wim H. Hesselink