TY  - JOUR
T1  - Some properties of equivalent maps
AU  - Maslova, Yu V
AU  - Zagorskaya, G R
AU  - Podkhodova, N S
AU  - Krylov, V V
Y1  - 2024-12-27
UR  - https://rep.herzen.spb.ru/publication/17679
N2  - The article examines one of the central objects of topological graph theory - the map. The very defnition of the concept of “map”, on which we will rely, is formulated in the works by A. K. Zvonkin, S. K. Lando, E. S. Krasko, A. V. Omelchenko. The equivalence relation on the set of maps is also introduced there. We focused on the search for invariant characteristics of these objects, which we formulated in the form of properties of equivalent maps. We have verifed that the number of faces, the degrees of the corresponding faces, and the types of corresponding edges and vertices are preserved for equivalent maps. Also, separately for maps of bouquets of circles, we defned the concept of a chord diagram corresponding to the vertex of the map, and proved that equivalent maps have chord diagrams of their vertices.