Geodesic
The ordered set of connected parts of a~polygonal graph
Izvestiya of Saratov University. Mathematics. Mechanics. Informatics, Tome 13 (2013) no. 2, pp. 44-51

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Under a polygonal graph is meant an oriented graph obtained from a cycle by some orientation of its edges. The set of all abstract (i.e. pairwise non-isomorphic) connected parts of a polygonal graph is ordered by graph embedding. Polygonal graphs are characterized for which this ordered set is a lattice. 
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V. N. Salii. The ordered set of connected parts of a~polygonal graph. Izvestiya of Saratov University. Mathematics. Mechanics. Informatics, Tome 13 (2013) no. 2, pp. 44-51. http://geodesic.mathdoc.fr/item/ISU_2013_13_2_a6/