[5] Eslahchi Ch. and Rahimi A.M., The k-Zero-Divisor Hypergraph of a Commutative Ring, Int. J. Math. Math. Sci. Art. 50875 (2007) 15.
[6] Beck I., Coloring of Commutative Rings, J. of Algebra, (1988) 208-226.
[7] Selvakumar K. and Ramanathana V., Classification of non-Local Rings with Genus One 3-zero-divisor Hypergraphs, Comm. Algebra, (2016) 275-284.
[8] Akbari S. and Mohammadian A., On the Zero-Divisor Graph of a Commutative Ring, J. Algebra, (2004) 847-855.
[9] Elele A.B. and Ulucak G., 3-Zero-Divisor Hypergraph Regarding an Ideal, 7 th International Conference on Modeling, Simulation, and Applied Optimization (ICMSAO), 2017.
[10] Badawi A., On 2-absorbing Ideals of Commutative Rings, Bull. Austral. Math. Soc.,75 (2007) 417-429.
3-Zero-Divisor Hypergraph with Respect to an Element in Multiplicative Lattice
Year 2019,
Volume: 40 Issue: 4, 792 - 801, 31.12.2019
Let be a multiplicative lattice and be a proper element of . We introduce the
3-zero-divisor hypergraph of with respect to which is a hypergraph whose vertices are
elements of the set where distinct vertices and are adjacent, that is, is a hyperedge if and only if . Throughout this paper,
the hypergraph is denoted by We investigate many properties of the
hypergraph over a multiplicative lattice. Moreover, we find a lower bound of
diameter of and obtain that is connected.
[5] Eslahchi Ch. and Rahimi A.M., The k-Zero-Divisor Hypergraph of a Commutative Ring, Int. J. Math. Math. Sci. Art. 50875 (2007) 15.
[6] Beck I., Coloring of Commutative Rings, J. of Algebra, (1988) 208-226.
[7] Selvakumar K. and Ramanathana V., Classification of non-Local Rings with Genus One 3-zero-divisor Hypergraphs, Comm. Algebra, (2016) 275-284.
[8] Akbari S. and Mohammadian A., On the Zero-Divisor Graph of a Commutative Ring, J. Algebra, (2004) 847-855.
[9] Elele A.B. and Ulucak G., 3-Zero-Divisor Hypergraph Regarding an Ideal, 7 th International Conference on Modeling, Simulation, and Applied Optimization (ICMSAO), 2017.
[10] Badawi A., On 2-absorbing Ideals of Commutative Rings, Bull. Austral. Math. Soc.,75 (2007) 417-429.
Ulucak, G. (2019). 3-Zero-Divisor Hypergraph with Respect to an Element in Multiplicative Lattice. Cumhuriyet Science Journal, 40(4), 792-801. https://doi.org/10.17776/csj.485085