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T\^ete-\`a-t\^ete graphs and relative t\^ete-\`a-t\^ete graphs wereintroduced by N. A'Campo in 2010 to model monodromies of isolated plane curves.By recent workof Fdez de Bobadilla, Pe Pereira and the author, they provide away of modeling the periodic mapping classes that leave some boundary componentinvariant. In this work we introduce the notion of general t\^ete-\`a-t\^etegraph and prove that they model all periodic mapping classes. We also describealgorithms that take a Seifert manifold and a horizontal surface and return at\^ete-\`a-t\^ete graph and vice versa.

General t\^ete-\`a-t\^ete graphs and Seifert manifolds