On constructing expander families of G-graphs
نویسندگان
چکیده
منابع مشابه
Expander Graphs
This paper will introduce expander graphs. Kolmogorov and Barzdin’s proof on the three dimensional realization of networks will be discussed as one of the first examples of expander graphs. The last section will discuss error correcting code as an application of expander graphs to computer science.
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متن کاملExpander Graphs
Let AG be the adjacency matrix of G. Let λ1 ≥ λ2 ≥ . . . ≥ λn be the eigenvalues of AG. Sometimes we will also be interested in the Laplacian matrix of G. This is defined to be LG = D−AG, where D is the diagonal matrix where Dvv equals the degree of the vertex v. For d-regular graphs, LG = dI −AG, and hence the eigenvalues of LG are d− λ1, d− λ2, . . . , d− λn. Lemma 1. • λ1 = d. • λ2 = λ3 = . ...
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We say that a graph G = (V,E) on n vertices is a β-expander for some constant β > 0 if every U ⊆ V of cardinality |U | ≤ n 2 satisfies |NG(U)| ≥ β|U | where NG(U) denotes the neighborhood of U . We explore the process of uniformly at random deleting vertices of a β-expander with probability n for some constant α > 0. Our main result implies that as n tends to infinity, the deletion process perf...
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Let G = (V,E) be an undirected d-regular graph, here, |V | = n, deg(u) = d for all u ∈ V . We will typically interpret the properties of expander graphs in an asymptotic sense. That is, there will be an infinite family of graphs G, with a growing number of vertices n. By “sparse”, we mean that the degree d of G should be very slowly growing as a function of n. When n goes to infinity (n → ∞), d...
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ژورنال
عنوان ژورنال: Ars Mathematica Contemporanea
سال: 2018
ISSN: 1855-3974,1855-3966
DOI: 10.26493/1855-3974.1537.97c