1. CMB 2014 (vol 57 pp. 573)
|Some Results on the Domination Number of a Zero-divisor Graph|
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.
Keywords:zero-divisor graph, domination number
2. CMB 2013 (vol 57 pp. 188)
|A Characterization of Bipartite Zero-divisor Graphs|
In this paper we obtain a characterization for all bipartite zero-divisor graphs of commutative rings $R$ with $1$, such that $R$ is finite or $|Nil(R)|\neq2$.
Keywords:zero-divisor graph, bipartite graph
3. CMB 2011 (vol 56 pp. 407)
|On Domination in Zero-Divisor Graphs|
We first determine the domination number for the zero-divisor graph of the product of two commutative rings with $1$. We then calculate the domination number for the zero-divisor graph of any commutative artinian ring. Finally, we extend some of the results to non-commutative rings in which an element is a left zero-divisor if and only if it is a right zero-divisor.
Keywords:zero-divisor graph, domination