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. 
@article{PDM_2024_4_a3,
     author = {O. V. Knyazev and D. V. Solomatin},
     title = {Multiplicative residue semigroups {with~planar~Cayley~graphs}},
     journal = {Prikladna\^a diskretna\^a matematika},
     pages = {36--44},
     publisher = {mathdoc},
     number = {4},
     year = {2024},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/PDM_2024_4_a3/}
}
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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/