Geodesic
Comparison of outerplanarity and~generalized~outerplanarity properties for~Cayley~graphs~of~planar~semigroups
Prikladnaâ diskretnaâ matematika, no. 2 (2024), pp. 20-26.

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

We have found two infinite series of semigroups whose Cayley graphs have an outerplanarity property equivalent to the generalized outerplanarity property of their Cayley graphs, but not equivalent to the planarity property, and one infinite series of semigroups whose Cayley graphs have a generalized outerplanarity property equivalent to the planarity property of their Cayley graphs, but not equivalent to outerplanarity. It is proved that the Cayley graph of a finite semigroup is not isomorphic to any of the forbidden Sedláček's subgraphs by the characteristic property of generalized outer planarity with any orientation and edge coloring.
Keywords: Chartrand — Harari graphs, Sedláček graphs, semigroups with planar Cayley graphs. 
@article{PDM_2024_2_a2,
     author = {D. V. Solomatin},
     title = {Comparison of outerplanarity and~generalized~outerplanarity properties {for~Cayley~graphs~of~planar~semigroups}},
     journal = {Prikladna\^a diskretna\^a matematika},
     pages = {20--26},
     publisher = {mathdoc},
     number = {2},
     year = {2024},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/PDM_2024_2_a2/}
}
TY  - JOUR
AU  - D. V. Solomatin
TI  - Comparison of outerplanarity and~generalized~outerplanarity properties for~Cayley~graphs~of~planar~semigroups
JO  - Prikladnaâ diskretnaâ matematika
PY  - 2024
SP  - 20
EP  - 26
IS  - 2
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/PDM_2024_2_a2/
LA  - ru
ID  - PDM_2024_2_a2
ER  - 
%0 Journal Article
%A D. V. Solomatin
%T Comparison of outerplanarity and~generalized~outerplanarity properties for~Cayley~graphs~of~planar~semigroups
%J Prikladnaâ diskretnaâ matematika
%D 2024
%P 20-26
%N 2
%I mathdoc
%U http://geodesic.mathdoc.fr/item/PDM_2024_2_a2/
%G ru
%F PDM_2024_2_a2
D. V. Solomatin. Comparison of outerplanarity and~generalized~outerplanarity properties for~Cayley~graphs~of~planar~semigroups. Prikladnaâ diskretnaâ matematika, no. 2 (2024), pp. 20-26. http://geodesic.mathdoc.fr/item/PDM_2024_2_a2/

[1] Chartrand G. and Harary F., “Planar permutation graphs”, Annales de l'I. H. P. Section B, 3:4 (1967), 433–438 | MR | Zbl

[2] Sedláček J., “A generalization of outerplanar graphs”, Časopis Pěst. Mat., 2:113 (1988), 213–218 (in Czech) | MR | Zbl

[3] Schietgat L., Ramon J., and Bruynooghe M., “A polynomial-time maximum common subgraph algorithm for outerplanar graphs and its application to chemoinformatics”, Ann. Math. Artif. Intell., 69 (2013), 343–376 | DOI | MR | Zbl

[4] Solomatin D. V., “Researches of semigroups with planar Cayley graphs: Results and problems”, Prikladnaya Diskretnaya Matematika, 2021, no. 54, 5–57 (in Russian) | MR | Zbl

[5] Solomatin D. V., “Direct products of cyclic monoids admitting outerplanar Cayley graphs and their generalizations”, Vestnik TvGU, Ser. Prikladnaya Matematika, 2023, no. 4, 43–56 (in Russian)

[6] Solomatin D. V., “Finitely generated semigroups with one defining relation and identity, admitting planar Cayley graphs”, Matematika i Informatika: Nauka i Obrazovanie, 2007, no. 6, 42–48 (in Russian) | MR

[7] Shneerson L. M., “Identities in semigroups with one defining relation”, Logika, Algebra i Vychisl. Matem., Ivanovo, 1972, no. 1–2, 139–156 (in Russian)

[8] Solomatin D. V., “Semigroups with outerplanar Cayley graphs”, Sib. Elektron. Matem. Izv., 8 (2011), 191–212 (in Russian) | MR

[9] Almeria J. C. and Sevilla A. M., “A linear algorithm to recognize maximal generalized outerplanar graphs”, Mathematica Bohemica, 122:3 (1997), 225–230 | DOI | MR

[10] Solomatin D. V., “Free partially commutative semigroups and n-fan semilattices with planar Cayley graphs”, Matematika i Informatika: Nauka i Obrazovanie, 2009, no. 8, 36–39 (in Russian) | MR

[11] Solomatin D. V., “On the admissibility of some graphs as Cayley graphs of semigroups”, Matematika i Informatika: Nauka i Obrazovanie, 2004, no. 4, 32–34 (in Russian)