Abstract
We discuss quantum graphs with the vertex coupling which violates the time-reversal invariance. For a simple type of this coupling in which the violation is in a sense maximum one we show that it leads to spectral properties determined in the high-energy regime by the graph topology. We illustrate this effect on examples which involve lattice graphs and loop arrays as well as finite graphs associated with Platonic solids. We also show that transport properties of such graphs may differ in the graph bulk and at the edges.
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