2 results
Maximizing the Index of Trees with Given Domination Number
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- Journal:
- Canadian Mathematical Bulletin / Volume 57 / Issue 3 / 01 September 2014
- Published online by Cambridge University Press:
- 20 November 2018, pp. 520-525
- Print publication:
- 01 September 2014
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- Article
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The index of a graph
$G$ is the maximum eigenvalue of its adjacency matrix 
$A\left( G \right)$. In this paper we characterize the extremal tree with given domination number that attains the maximum index.
Some Results on the Domination Number of a Zero-divisor Graph
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- Journal:
- Canadian Mathematical Bulletin / Volume 57 / Issue 3 / 01 September 2014
- Published online by Cambridge University Press:
- 20 November 2018, pp. 573-578
- Print publication:
- 01 September 2014
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- Article
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- You have access
- Export citation
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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
$\Gamma \left( {R}/{I}\; \right)$ and 
${{\Gamma }_{1}}\left( R \right)$, and the domination numbers of 
$\Gamma \left( R \right)$ and 
$\Gamma \left( R\left[ x,\,\alpha ,\,\delta \right] \right)$, where 
$R\left[ x,\,\alpha ,\,\delta \right]$ is the Ore extension of 
$R$, are studied.
