Abstract
Let us say that a Cayley graph Γ of a group G of order n is a Černý Cayley graph if every synchronizing automaton containing Γ as a subgraph with the same vertex set admits a synchronizing word of length at most (n−1)2. In this paper we use the representation theory of groups over the rational numbers to obtain a number of new infinite families of Černý Cayley graphs.
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Steinberg, B. Černý’s conjecture and group representation theory. J Algebr Comb 31, 83–109 (2010). https://doi.org/10.1007/s10801-009-0185-0
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DOI: https://doi.org/10.1007/s10801-009-0185-0