Some results on the domination number of a zero-divisor graph. (English) Zbl 1302.05213
Summary: In this paper, we investigate the domination, total domination and semi-total domination numbers of a zero-divisor graph of a commutative Noetherian ring. Also, some relations between the domination numbers of \(\Gamma(R/I)\) and \(\Gamma_I(R)\), and the domination numbers of \(\Gamma(R)\) and \(\Gamma(R[x,\alpha,\delta])\), where \(R[x,\alpha,\delta]\) is the Ore extension of \(R\), are studied.
MSC:
| 05E40 | Combinatorial aspects of commutative algebra |
| 05C69 | Vertex subsets with special properties (dominating sets, independent sets, cliques, etc.) |
| 05C75 | Structural characterization of families of graphs |
| 13H10 | Special types (Cohen-Macaulay, Gorenstein, Buchsbaum, etc.) |
