Flexibility and movability in Cayley graphs

2019/11/14 by Biswas, Arindam
#05C15 #05C25 #05C38 #05C42 #52C25 #70B15 #Combinatorics (math.CO) #FOS: Mathematics

paper · doi:10.48550/arxiv.1911.06261

Abstract

Let \mathbfΓ = (V,E) be a (non-trivial) finite graph with λ: E → ℝ₊, an edge labelling of \mathbfΓ. Let ρ: V→ ℝ² be a map which preserves the edge labelling. The graph \mathbfΓ is said to be flexible if there exists an infinite number of such maps (upto equivalence by rigid transformations) and it is said to be movable if there exists an infinite number of injective maps. We study movability of Cayley graphs and construct regular moving graphs of all degrees. Further, we give explicit constructions of "dense", movable graphs.

Related

• Stable cuts, NAC-colourings and flexible realisations of graphs
• Conformal Rigidity and Spectral Embeddings of Graphs
• Locally infinite graphs and symmetries
• On the separation profile of infinite graphs
• Generalized Cayley Graphs and Cellular Automata over them