THE SQUARE MAPPING GRAPHS OF THE RING $\mathbb{Z}$ n [ i ]
Yangjiang Wei, Gaohua Tang · 2016
In this paper, we investigate some properties of the square mapping graphs Γ(n) of $\mathbb{Z}$ n[i], the ring of Gaussian integers modulo n. Using the method of number theory, graph theory and group theory, we obtain the in-degree of 0 and 1 . Moreover, we give the complete characterizations in terms of n in which Γ2(n) is semiregular, where Γ2(n) is induced by all the zero-divisors of $\mathbb{Z}$ n[i]. The formulas on the heights of vertices in Γ(n) are also obtained. This paper extends results concerning the square mapping graphs of $\mathbb{Z}$ n given by Somer.