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In this paper, we consider terminal reflexive polytopes arising from finitedirected graphs and study the problem of deciding which directed graphs yieldsmooth Fano polytopes. We show that any centrally symmetric or pseudo-symmetricsmooth Fano polytopes can be obtained from directed graphs. Moreover, by usingdirected graphs, we provide new examples of smooth Fano polytopes whosecorresponding varieties admit K\"ahler--Einstein metrics.

Smooth Fano polytopes arising from finite directed graphs