{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,5,14]],"date-time":"2025-05-14T02:28:24Z","timestamp":1747189704785,"version":"3.40.5"},"reference-count":25,"publisher":"World Scientific Pub Co Pte Ltd","issue":"08","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Int. J. Algebra Comput."],"published-print":{"date-parts":[[2023,12]]},"abstract":"<jats:p> Principal fully irreducible outer automorphisms were introduced in [Y.\u00a0Algom-Kfir, I.\u00a0Kapovich and C.\u00a0Pfaff, Stable strata of geodesics in outer space, Int. Math. Res. Not.\u00a02019(14) (2019) 4549\u20134578] to emulate principal pseudo-Anosov surface homeomorphisms, i.e. those whose attracting and repelling invariant foliations have only 3-pronged singularities. It is proved in [Y.\u00a0Algom-Kfir, I.\u00a0Kapovich and C.\u00a0Pfaff, Stable strata of geodesics in outer space, Int. Math. Res. Not.\u00a02019(14) (2019) 4549\u20134578] that these outer automorphisms semi-mimic principal pseudo-Anosov surface homeomorphisms in important ways. We prove here which rank-3 graphs carry train track representatives of principal fully irreducible outer automorphisms. 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