| Title: | Constructing reflection-symmetric flexible realisations of graphs |
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| Authors: | ID Dewar, Sean (Author)
ID Grasegger, Georg (Author)
ID Legerský, Jan (Author) |
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| Files: |  AMC_Dewar,_Grasegger,_Legersky_2026.pdf (571,84 KB)
MD5: 0A693C4A65A4054957617784C3826350
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| Language: | English |
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| Work type: | Article |
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| Typology: | 1.01 - Original Scientific Article |
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| Organization: | ZUP - University of Primorska Press
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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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| Keywords: | Flexible framework, rigidity, reflection symmetry, edge coloring |
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| Publication status: | Published |
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| Publication version: | Version of Record |
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| Publication date: | 04.06.2026 |
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| Publisher: | Založba Univerze na Primorskem |
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| Year of publishing: | 2026 |
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| Number of pages: | 26 str. |
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| Numbering: | Vol. 26, no. 3, [article no.] P3.05 |
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| PID: | 20.500.12556/RUP-23514  |
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| UDC: | 51 |
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| eISSN: | 1855-3974 |
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| DOI: | 10.26493/1855-3974.3445.d9e |
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| Publication date in RUP: | 18.08.2026 |
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| Views: | 25 |
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| Downloads: | 1 |
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