Geodesic
On the Spectral Gap and the Diameter of Cayley Graphs
Informatics and Automation, Analytic and Combinatorial Number Theory, Tome 314 (2021), pp. 318-337

Voir la notice de l'article provenant de la source Math-Net.Ru

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. 
@article{TRSPY_2021_314_a15,
     author = {I. D. Shkredov},
     title = {On the {Spectral} {Gap} and the {Diameter} of {Cayley} {Graphs}},
     journal = {Informatics and Automation},
     pages = {318--337},
     publisher = {mathdoc},
     volume = {314},
     year = {2021},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TRSPY_2021_314_a15/}
}
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I. D. Shkredov. On the Spectral Gap and the Diameter of Cayley Graphs. Informatics and Automation, Analytic and Combinatorial Number Theory, Tome 314 (2021), pp. 318-337. http://geodesic.mathdoc.fr/item/TRSPY_2021_314_a15/