On the line graph of the zero divisor graph for the ring of Gaussian integers modulo \(n\) (Q666536)
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scientific article; zbMATH DE number 6013088
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | On the line graph of the zero divisor graph for the ring of Gaussian integers modulo \(n\) |
scientific article; zbMATH DE number 6013088 |
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On the line graph of the zero divisor graph for the ring of Gaussian integers modulo \(n\) (English)
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8 March 2012
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Summary: Let \(\Gamma(\mathbb Z_n[i])\) be the zero divisor graph for the ring of the Gaussian integers modulo \(n\). Several properties of the line graph of \(\Gamma(\mathbb Z_n[i]), L(\Gamma(\mathbb Z_n[i]))\) are studied. It is determined when \(L(\Gamma(\mathbb Z_n[i]))\) is Eulerian, Hamiltonian, or planar. The girth, the diameter, the radius, and the chromatic and clique numbers of this graph are found. In addition, the domination number of \(L(\Gamma(\mathbb Z_n[i]))\) is given when \(n\) is a power of a prime. On the other hand, several graph invariants for \(\Gamma(\mathbb Z_n[i])\) are also determined.
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zero divisor graphs of commutative rings
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0.9630958
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0.96050066
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0.9524121
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0.9489543
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0.9469806
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0.91543555
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0.8989839
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