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- W2027118220 abstract "Abstract The expansion constant of a simple graph G of order n is defined as where $E(S, overline {S})$ denotes the set of edges in G between the vertex subset S and its complement $overline {S}$ . An expander family is a sequence { G i } of d -regular graphs of increasing order such that h ( G i )>ϵ for some fixed ϵ>0. Existence of such families is known in the literature, but explicit construction is nontrivial. A folklore theorem states that there is no expander family of circulant graphs only. In this note, we provide an elementary proof of this fact by first estimating the second largest eigenvalue of a circulant graph, and then employing Cheeger’s inequalities where G is a d -regular graph and λ 2 ( G ) denotes the second largest eigenvalue of G . Moreover, the associated equality cases are discussed." @default.
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- W2027118220 date "2010-11-17" @default.
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- W2027118220 title "NONEXISTENCE OF A CIRCULANT EXPANDER FAMILY" @default.
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- W2027118220 doi "https://doi.org/10.1017/s0004972710001644" @default.
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