Geodesic
On the Spectral Gap and the Diameter of Cayley Graphs
Trudy Matematicheskogo Instituta imeni V.A. Steklova, Analytic and Combinatorial Number Theory, Tome 314 (2021), pp. 318-337.

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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. 
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     author = {I. D. Shkredov},
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I. D. Shkredov. On the Spectral Gap and the Diameter of Cayley Graphs. Trudy Matematicheskogo Instituta imeni V.A. Steklova, Analytic and Combinatorial Number Theory, Tome 314 (2021), pp. 318-337. http://geodesic.mathdoc.fr/item/TM_2021_314_a15/

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