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Research Article

Oriented 2-Cell Embeddings of a Graph and Their Symmetry Classification: Generating Algorithms and Case Study of the Möbius-Kantor Graph

E. Lijnen* and A. Ceulemans

Departement Chemie, K.U. Leuven, Celestijnenlaan 200F, B-3001 Leuven, Belgium

J. Chem. Inf. Comput. Sci., 2004, 44 (5), pp 1552–1564

DOI: 10.1021/ci049865c

Publication Date (Web): August 18, 2004

Corresponding author phone: +32 16 32 73 80; fax: +32 16 32 79 92; e-mail: erwin.lijnen@chem.kuleuven.ac.be.

Abstract

We discuss a method to derive all symmetry-distinct oriented 2-cell embeddings of a given graph and classify them based on their symmetry. As an example, we apply the algorithm to the highly symmetrical trivalent Möbius-Kantor graph. Considering the derived 2-cell embeddings as carbon networks leads to some interesting negative curvature carbon allotropes.

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