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Prikladnaya Diskretnaya Matematika, 2024, Number 64, Pages 20–26
DOI: https://doi.org/10.17223/20710410/64/2
(Mi pdm835)
 

Theoretical Backgrounds of Applied Discrete Mathematics

Comparison of outerplanarity and generalized outerplanarity properties for Cayley graphs of planar semigroups

D. V. Solomatin

Omsk State Pedagogical University, Omsk, Russia
References:
Abstract: 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.
Document Type: Article
UDC: 512.532
Language: Russian
Citation: D. V. Solomatin, “Comparison of outerplanarity and generalized outerplanarity properties for Cayley graphs of planar semigroups”, Prikl. Diskr. Mat., 2024, no. 64, 20–26
Citation in format AMSBIB
\Bibitem{Sol24}
\by D.~V.~Solomatin
\paper Comparison of outerplanarity and~generalized~outerplanarity properties for~Cayley~graphs~of~planar~semigroups
\jour Prikl. Diskr. Mat.
\yr 2024
\issue 64
\pages 20--26
\mathnet{http://mi.mathnet.ru/pdm835}
\crossref{https://doi.org/10.17223/20710410/64/2}
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    Прикладная дискретная математика
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