Visualization of Automorphisms and Vertex-Symmetry
A heuristic for the visualization of arbitrary automorphisms of a graph by two-dimensional drawings is presented. The restriction of the drawing to a subgraph induced by an orbit of the automorphism is according to a symmetry of the plane. For a vertex-symmetric graph, a collection of drawings for a set of automorphisms which generate a transitive group on the vertices shows this symmetry property.
KeywordsRotation Symmetry Jordan Curve Straight Line Segment Transitive Group Petersen Graph
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- 1.Norman Biggs. Algebraic Graph Theory. Cambridge University Press, 2nd edition, 1993.Google Scholar
- 3.B. A. Dubrovin, A. T. Fomenko, and S. P. Novikov. Modern Geometry—Methods and Applications. Part I. The Geometry of Surfaces, Transformation Groups, and Fields. Springer-Verlag, 1984.Google Scholar
- 7.Michael Sampels. Representation of vertex-symmetric interconnection networks. In R. Wyrzykowski, H. Piech, and J. Szopa, editors, Proceedings of the 2nd International Conference on Parallel Processing & Applied Mathematics (PPAM’ 97), volume 1, pages 226–237. PCz IMI, 1997.Google Scholar
- 8.Martin Schönert et al. GAP — Groups, Algorithms and Programming. Lehrstuhl D für Mathematik, RWTH Aachen, Germany, 5th edition, 1995.Google Scholar