The cubic mapping graph for the ring of Gaussian integers modulo $n$

Wei, Yangjiang ; Nan, Jizhu ; Tang, Gaohua

Czechoslovak Mathematical Journal, Tome 61 (2011) no. 4, pp. 1023-1036.

Résumé

The article studies the cubic mapping graph $\mathrm{\Gamma }(n)$ of ${\mathbb{Z}}_n[\mathrm{i}]$, the ring of Gaussian integers modulo $n$. For each positive integer $n>1$, the number of fixed points and the in-degree of the elements $\bar{1}$ and $\bar{0}$ in $\mathrm{\Gamma }(n)$ are found. Moreover, complete characterizations in terms of $n$ are given in which ${\mathrm{\Gamma }}_2(n)$ is semiregular, where ${\mathrm{\Gamma }}_2(n)$ is induced by all the zero-divisors of ${\mathbb{Z}}_n[\mathrm{i}]$.

Détail

DOI : 10.1007/s10587-011-0045-7

Classification : 05C05, 11A07, 13M05
Mots-clés : Gaussian integers modulo $n$; cubic mapping graph; fixed point; semiregularity