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arXiv · 2408.06928

Constructing reflection-symmetric flexible realisations of graphs

Sean Dewar·Georg Grasegger·Jan Legerský
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Abstract

We study reflection-symmetric realisations of symmetric graphs in the plane that allow a continuous symmetry and edge-length preserving deformation. To do so, we identify a necessary combinatorial condition on graphs with reflection-symmetric flexible realisations. This condition is based on a specific type of edge colouring, where edges are assigned one of three colours in a symmetric way. From some of these colourings we also construct concrete reflection-symmetric realisations with their corresponding symmetry preserving motion. We study also a specific class of reflection-symmetric realisations consisting of triangles and parallelograms.

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Sean Dewar, Georg Grasegger, Jan Legerský. 2024-08-13. Constructing reflection-symmetric flexible realisations of graphs. https://doi.org/10.26493/1855-3974.3445.d9e

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