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Trudy Mat. Inst. Steklova, 2021, Volume 314, Pages 318–337 (Mi tm4199)  

On the Spectral Gap and the Diameter of Cayley Graphs

I. D. Shkredov

Steklov Mathematical Institute of Russian Academy of Sciences, ul. Gubkina 8, Moscow, 119991 Russia

Abstract: We obtain a new bound connecting the first nontrivial eigenvalue of the Laplace operator on a graph and the diameter of the graph. This bound is effective for graphs with small diameter as well as for graphs with the number of maximal paths comparable to the expected value.

Funding Agency Grant Number
Russian Science Foundation 19-11-00001
This work is supported by the Russian Science Foundation under grant 19-11-00001.


DOI: https://doi.org/10.4213/tm4199

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English version:
Proceedings of the Steklov Institute of Mathematics, 2021, 314, 307–324

Bibliographic databases:

UDC: 511.218+511.33
Received: April 22, 2020
Revised: March 5, 2021
Accepted: April 23, 2021

Citation: I. D. Shkredov, “On the Spectral Gap and the Diameter of Cayley Graphs”, Analytic and Combinatorial Number Theory, Collected papers. In commemoration of the 130th birth anniversary of Academician Ivan Matveevich Vinogradov, Trudy Mat. Inst. Steklova, 314, Steklov Math. Inst., Moscow, 2021, 318–337; Proc. Steklov Inst. Math., 314 (2021), 307–324

Citation in format AMSBIB
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\paper On the Spectral Gap and the Diameter of Cayley Graphs
\inbook Analytic and Combinatorial Number Theory
\bookinfo Collected papers. In commemoration of the 130th birth anniversary of Academician Ivan Matveevich Vinogradov
\serial Trudy Mat. Inst. Steklova
\yr 2021
\vol 314
\pages 318--337
\publ Steklov Math. Inst.
\publaddr Moscow
\mathnet{http://mi.mathnet.ru/tm4199}
\crossref{https://doi.org/10.4213/tm4199}
\transl
\jour Proc. Steklov Inst. Math.
\yr 2021
\vol 314
\pages 307--324
\crossref{https://doi.org/10.1134/S0081543821040167}
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  • Труды Математического института им. В. А. Стеклова Proceedings of the Steklov Institute of Mathematics
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