Geodesic
Planar varieties of semigroups
Sibirskie èlektronnye matematičeskie izvestiâ, Tome 12 (2015), pp. 232-247

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

We study the property of planarity of Cayley graphs for varieties of semigroups. It is proved that the variety of semigroups with zero multiplication $\mathrm{ var}\{xy=zt\}$, the variety of left zero semigroups $\mathrm{ var}\{xy=x\}$ and the variety $\mathrm{ var}\{xy=xz\}$ are the only non-trivial planar variety of semigroups. We find the ranks of planarity for some important series of varieties of semigroups.
Keywords: semigroup, Cayley graph, variety of semigroups, planar graph, rank of planarity. 
@article{SEMR_2015_12_a8,
     author = {D. V. Solomatin},
     title = {Planar varieties of semigroups},
     journal = {Sibirskie \`elektronnye matemati\v{c}eskie izvesti\^a},
     pages = {232--247},
     publisher = {mathdoc},
     volume = {12},
     year = {2015},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/SEMR_2015_12_a8/}
}
TY  - JOUR
AU  - D. V. Solomatin
TI  - Planar varieties of semigroups
JO  - Sibirskie èlektronnye matematičeskie izvestiâ
PY  - 2015
SP  - 232
EP  - 247
VL  - 12
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/SEMR_2015_12_a8/
LA  - ru
ID  - SEMR_2015_12_a8
ER  - 
%0 Journal Article
%A D. V. Solomatin
%T Planar varieties of semigroups
%J Sibirskie èlektronnye matematičeskie izvestiâ
%D 2015
%P 232-247
%V 12
%I mathdoc
%U http://geodesic.mathdoc.fr/item/SEMR_2015_12_a8/
%G ru
%F SEMR_2015_12_a8
D. V. Solomatin. Planar varieties of semigroups. Sibirskie èlektronnye matematičeskie izvestiâ, Tome 12 (2015), pp. 232-247. http://geodesic.mathdoc.fr/item/SEMR_2015_12_a8/