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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 Categories:05C75, 13H10 |
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 Categories:13AXX, 05C25 |
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 Categories:13AXX, 05C69 |