Note on the girth of Ramanujan graphs (Q920107)
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scientific article; zbMATH DE number 4162912
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Note on the girth of Ramanujan graphs |
scientific article; zbMATH DE number 4162912 |
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Note on the girth of Ramanujan graphs (English)
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1990
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A Ramanujan graph in a finite k-regular graph all eigenvalues of which, other than \(\pm k\), have modulus at most \(2\sqrt{k-1}\). Such graphs are well-suited for the construction of expanders. \textit{A. Lubotzky, R. Phillips} and \textit{P. Sarnak} [Combinatorica 8, No.3, 261-277 (1988; Zbl 0661.05035)] presented, for infinitely many k, an explicit construction of such graphs with order n and girth g asymptotically satisfying \((\log_{k-1}n)/g\leq 3/4\). The author shows this bound to be sharp.
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Ramanujan graph
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eigenvalues
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expanders
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girth
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