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.
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
\Bibitem{Shk21}
\by I.~D.~Shkredov
\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}
\elib{https://elibrary.ru/item.asp?id=47510615}
\transl
\jour Proc. Steklov Inst. Math.
\yr 2021
\vol 314
\pages 307--324
\crossref{https://doi.org/10.1134/S0081543821040167}
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Linking options:
https://www.mathnet.ru/eng/tm4199
https://doi.org/10.4213/tm4199
https://www.mathnet.ru/eng/tm/v314/p318
This publication is cited in the following 2 articles:
I. D. Shkredov, “On multiplicative energy of subsets of varieties”, Can. J. Math., 75:1 (2022), 322–340
I. D. Shkredov, “Non-commutative methods in additive combinatorics and number theory”, Russian Math. Surveys, 76:6 (2021), 1065–1122
Citation in format AMSBIB
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