## Some properties of the zero-divisor graph for the ring of Gaussian integers modulo $$n$$.(English)Zbl 1213.13019

Summary: This paper is a continuation for the study of the zero-divisor graph for the ring of Gaussian integers modulo $$n$$, $$\Gamma (\mathbb Z_{n}[i])$$ in [E. A. Osba, S. Al-Addasi and N. A. Jaradeh, Commun. Algebra 36, No. 10, 3865–3877 (2008; Zbl 1151.05042)]. It is investigated, when is $$\Gamma (\mathbb Z_{n}[i])$$ locally $$H$$, Hamiltonian or bipartite graph? A full characterisation for the chromatic number and the radius is also given.

### MSC:

 13A99 General commutative ring theory 05C15 Coloring of graphs and hypergraphs

Zbl 1151.05042
Full Text:

### References:

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