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Search: All articles in the CMB digital archive with keyword domination

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1. CMB 2015 (vol 58 pp. 271)

 On Domination of Zero-divisor Graphs of Matrix Rings We study domination in zero-divisor graphs of matrix rings over a commutative ring with $1$. Keywords:vector space, linear transformation, zero-divisor graph, domination, local ringCategory:05C69

2. CMB 2014 (vol 57 pp. 573)

Kiani, Sima; Maimani, Hamid Reza; Nikandish, Reza
 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 numberCategories:05C75, 13H10

3. CMB 2014 (vol 57 pp. 520)

Guo, Guangquan; Wang, Guoping
 Maximizing the Index of Trees with Given Domination Number The index of a graph $G$ is the maximum eigenvalue of its adjacency matrix $A(G)$. In this paper we characterize the extremal tree with given domination number that attains the maximum index. Keywords:trees, spectral radius, index, domination numberCategory:05C50

4. CMB 2013 (vol 57 pp. 141)

Mukwembi, Simon
 Size, Order, and Connected Domination We give a sharp upper bound on the size of a triangle-free graph of a given order and connected domination. Our bound, apart from strengthening an old classical theorem of Mantel and of TurÃ¡n , improves on a theorem of Sanchis. Further, as corollaries, we settle a long standing conjecture of Graffiti on the leaf number and local independence for triangle-free graphs and answer a question of Griggs, Kleitman and Shastri on a lower bound of the leaf number in triangle-free graphs. Keywords:size, connected domination, local independence number, leaf numberCategory:05C69

5. 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, dominationCategories:13AXX, 05C69