Geodesic
Primitive digraphs with large exponents and slowly synchronizing automata
Zapiski Nauchnykh Seminarov POMI, Combinatorics and graph theory. Part IV, Tome 402 (2012), pp. 9-39

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We exhibit several infinite series of synchronizing automata. The minimum length of reset words for each of the automata is close to the state number squared. All these automata are tightly related to primitive directed graphs with large exponents. 
@article{ZNSL_2012_402_a1,
     author = {D. S. Ananichev and M. V. Volkov and V. V. Gusev},
     title = {Primitive digraphs with large exponents and slowly synchronizing automata},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {9--39},
     publisher = {mathdoc},
     volume = {402},
     year = {2012},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_2012_402_a1/}
}
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D. S. Ananichev; M. V. Volkov; V. V. Gusev. Primitive digraphs with large exponents and slowly synchronizing automata. Zapiski Nauchnykh Seminarov POMI, Combinatorics and graph theory. Part IV, Tome 402 (2012), pp. 9-39. http://geodesic.mathdoc.fr/item/ZNSL_2012_402_a1/