Geodesic
Graphs with framed vertices
Zapiski Nauchnykh Seminarov POMI, Geometry and topology. Part 12, Tome 415 (2013), pp. 103-108

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We reduce the topology classification problem of finite graphs with framed vertices to a topology classification problem of plane trees. 
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     author = {V. M. Nezhinskij and Yu. V. Maslova},
     title = {Graphs with framed vertices},
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     pages = {103--108},
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     year = {2013},
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     url = {http://geodesic.mathdoc.fr/item/ZNSL_2013_415_a12/}
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V. M. Nezhinskij; Yu. V. Maslova. Graphs with framed vertices. Zapiski Nauchnykh Seminarov POMI, Geometry and topology. Part 12, Tome 415 (2013), pp. 103-108. http://geodesic.mathdoc.fr/item/ZNSL_2013_415_a12/