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Search: MSC category 05C69 ( Dominating sets, independent sets, cliques )

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1. 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 Turán , 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 number
Category:05C69

2. CMB 2011 (vol 56 pp. 407)

Rad, Nader Jafari; Jafari, Sayyed Heidar; Mojdeh, Doost Ali
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

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