Connective constants and height functions for Cayley graphs
نویسندگان
چکیده
منابع مشابه
Locality of Connective Constants, Ii. Cayley Graphs
The connective constant μ(G) of an infinite transitive graph G is the exponential growth rate of the number of self-avoiding walks from a given origin. In earlier work of Grimmett and Li, a locality theorem was proved for connective constants, namely, that the connective constants of two graphs are close in value whenever the graphs agree on a large ball around the origin. A condition of the th...
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The connective constant μ(G) of a quasi-transitive graph G is the exponential growth rate of the number of self-avoiding walks from a given origin. We prove a locality theorem for connective constants, namely, that the connective constants of two graphs are close in value whenever the graphs agree on a large ball around the origin. The proof exploits a generalized bridge decomposition of self-a...
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Bounds are proved for the connective constant μ of an infinite, connected, ∆-regular graph G. The main result is that μ ≥ √ ∆− 1 if G is vertex-transitive and simple. This inequality is proved subject to weaker conditions under which it is sharp.
متن کاملStrict Inequalities for Connective Constants of Transitive Graphs
The connective constant of a graph is the exponential growth rate of the number of self-avoiding walks starting at a given vertex. Strict inequalities are proved for connective constants of vertex-transitive graphs. First, the connective constant decreases strictly when the graph is replaced by a nontrivial quotient graph. Second, the connective constant increases strictly when a quasitransitiv...
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Abstract. Let G be a finite abelian group of exponent m ≥ 2. For subsets A,S ⊆ G, denote by ∂S(A) the number of edges from A to its complement G \ A in the directed Cayley graph, induced by S on G. We show that if S generates G, and A is non-empty, then ∂S(A) ≥ e m |A| ln |G| |A| . Here the coefficient e = 2.718 . . . is best possible and cannot be replaced with a number larger than e. For homo...
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ژورنال
عنوان ژورنال: Transactions of the American Mathematical Society
سال: 2017
ISSN: 0002-9947,1088-6850
DOI: 10.1090/tran/7166