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In 2020, through his work on a numerical evaluation for the aromaticity, the second author conjectured that the eigenvalues of a directed graph corresponding to polyacen (linearly connected r hexagons) would draw ⌊(r+1)/2⌋ hexagons on the complex plane. In this letter, we would like to introduce operations on directed graphs and prove his conjecture in a general form.
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Kashihara et al. (2023) studied this question.
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