Approximating graphs with polynomial
growth

Сейфтер, Норберт; Woess, Wolfgang

doi:10.1017/s001708950001003x

Cited by 4 publications

(3 citation statements)

References 11 publications

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“…For an almost-transitive graph Γ, i.e, if the automorphism group of Γ acts on it with finitely many orbits we have the following equivalence [16]: if Γ is an almost-transitive graphs whose growth is at most polynomial then its growth is at least polynomial. Indeed, almost-transitive graphs whose growth is at most polynomial are doubling graphs.…”

Section: Complete Coveragementioning

confidence: 99%

Boolean Percolation on Doubling Graphs

2019

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We consider the discrete Boolean model of percolation on graphs satisfying a doubling metric condition. We study sufficient conditions on the distribution of the radii of balls placed at the points of a Bernoulli point process for the absence of percolation, provided that the retention parameter of the underlying point process is small enough. We exhibit three families of interesting graphs where the main result of this work holds. Finally, we give sufficient conditions for ergodicity of the discrete Boolean model of percolation.

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Section: Complete Coveragementioning

confidence: 99%

Boolean Percolation on Doubling Graphs

2019

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“…One may deduce a classification of tetravalent one-regular Cayley graphs on dihedral groups from Kwak and Oh [16] and Wang et al [32,33]. Malnič et al [21] constructed an infinite family of infinite oneregular graphs, which steps into the important territory of symmetry in infinite graphs; see also [19,31] for some more results related to this topic. Let p and q be primes.…”

Section: Introductionmentioning

confidence: 99%

Tetravalent one-regular graphs of order 2pq

Zhou

Feng

2008

J Algebr Comb

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“…Furthermore, all 4-valent one-regular graphs of order 2pq were classified by Zhou and Feng [43]. On the other hand, Malnič et al [24] constructed an infinite family of infinite one-regular graphs; see also [21,31] for related results.…”

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confidence: 99%

Arc-regular cubic graphs of order four times an odd integer

Conder

Feng

2011

J Algebr Comb

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A graph is arc-regular if its automorphism group acts sharply-transitively on the set of its ordered edges. This paper answers an open question about the existence of arc-regular 3-valent graphs of order 4m where m is an odd integer. Using the Gorenstein-Walter theorem, it is shown that any such graph must be a normal cover of a base graph, where the base graph has an arc-regular group of automorphisms that is isomorphic to a subgroup of Aut(PSL(2, q)) containing PSL(2, q) for some odd prime-power q. Also a construction is given for infinitely many such graphsnamely a family of Cayley graphs for the groups PSL(2, p 3 ) where p is an odd prime; the smallest of these has order 9828.

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Approximating graphs with polynomial growth

Abstract: Abstract. Let X be an in®nite, locally ®nite, almost transitive graph with polynomial growth. We show that such a graph X is the inverse limit of an in®nite sequence of ®nite graphs satisfying growth conditions which are closely related to growth properties of the in®nite graph X.

Cited by 4 publications

References 11 publications

Boolean Percolation on Doubling Graphs

Boolean Percolation on Doubling Graphs

Tetravalent one-regular graphs of order 2pq

Arc-regular cubic graphs of order four times an odd integer

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