Small cancellation labellings of some infinite graphs and applications
نویسندگان
چکیده
منابع مشابه
Small Cancellation Labellings of Some Infinite Graphs and Applications
We construct small cancellation labellings for some infinite sequences of finite graphs of bounded degree. We use them to define infinite graphical small cancellation presentations of groups. This technique allows us to provide examples of groups with exotic properties: • We construct the first examples of finitely generated coarsely nonamenable groups (that is, groups without Guoliang Yu’s Pro...
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There are many results on edge-magic, and vertex-magic, labellings of finite graphs. Here we consider magic labellings of countably infinite graphs over abelian groups. We also give an example of a finite connected graph that is edge-magic over one, but not over all, abelian groups of the appropriate order.
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A total labelling of a graph over an abelian group is a bijection from the set of vertices and edges onto the set of group elements. A labelling can be used to define a weight for each edge and for each vertex of finite degree. A labelling is edge-magic if all the edges have the same weight and vertex-magic if all the vertices are finite degree and have the same weight. We exhibit magic labelli...
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Let G = (V,E) be a connected undirected graph and S a subset of vertices. If for all vertices v ∈ V , the sets Br(v) ∩ S are all nonempty and different, where Br(v) denotes the set of all points within distance r from v, then we call S an r-identifying code. We give constructive upper bounds on the best possible density of r-identifying codes in four infinite regular graphs, for small values of r.
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ژورنال
عنوان ژورنال: Acta Mathematica
سال: 2020
ISSN: 0001-5962,1871-2509
DOI: 10.4310/acta.2020.v225.n1.a3