Geodesic
Multiplicative residue semigroups with~planar~Cayley~graphs
Prikladnaâ diskretnaâ matematika, no. 4 (2024), pp. 36-44.

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We study multiplicative residue semigroups that admit planar Cayley graphs. It is proved that the multiplicative semigroup of the residue ring $\mathbb{Z}_n$ admits a planar Cayley graph if and only if $n=4,6,8$ or $n$ is a prime number. Examples of minimal systems of generators of multiplicative residue semigroups with respect to some modules and their Cayley graphs are given, illustrating the obtained results.
Mots-clés : residue
Keywords: multiplicative semigroup of residues, generating semigroup set, Cayley graph of semigroup, planar graph. 
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O. V. Knyazev; D. V. Solomatin. Multiplicative residue semigroups with~planar~Cayley~graphs. Prikladnaâ diskretnaâ matematika, no. 4 (2024), pp. 36-44. http://geodesic.mathdoc.fr/item/PDM_2024_4_a3/

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