Geodesic
On perfect colorings of infinite multipath graphs
Sibirskie èlektronnye matematičeskie izvestiâ, Tome 17 (2020), pp. 2084-2095

Voir la notice de l'article provenant de la source Math-Net.Ru

A coloring of vertices of a given graph is called perfect if the color structure of each sphere of radius $1$ in the graph depends only on the color of the sphere center. Let $n$ be a positive integer. We consider a lexicographic product of the infinite path graph and a graph $G$ that can be either the complete or empty graph on $n$ vertices. We give a complete description of perfect colorings with an arbitrary number of colors of such graph products.
Keywords: perfect coloring, equivalent colors, infinite multipath graph.
Mots-clés : equitable partition 
@article{SEMR_2020_17_a77,
     author = {M. A. Lisitsyna and S. V. Avgustinovich and O. G. Parshina},
     title = {On perfect colorings of infinite multipath graphs},
     journal = {Sibirskie \`elektronnye matemati\v{c}eskie izvesti\^a},
     pages = {2084--2095},
     publisher = {mathdoc},
     volume = {17},
     year = {2020},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/SEMR_2020_17_a77/}
}
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M. A. Lisitsyna; S. V. Avgustinovich; O. G. Parshina. On perfect colorings of infinite multipath graphs. Sibirskie èlektronnye matematičeskie izvestiâ, Tome 17 (2020), pp. 2084-2095. http://geodesic.mathdoc.fr/item/SEMR_2020_17_a77/