Let $L$ be a lattice with the least element $0$. An element $x\in L$ is a zero divisor if $x\wedge y=0$ for some $y\in L^*=L\setminus \left\{0\right\}$. The set of all zero divisors is denoted by $Z(L)$. We associate a simple graph $\Gamma(L)$ to $L$ with vertex set $Z(L)^*=Z(L)\setminus \left\{0\right\}$, the set of non-zero zero divisors of $L$ and distinct $x,y\in Z(L)^*$ are adjacent if and only if $x\wedge y=0$. In this paper, we obtain certain properties and diameter and girth of the zero divisor graph $\Gamma(L)$. Also we find a dominating set and the domination number of the zero divisor graph $\Gamma(L)$.
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Tamizh Chelvam, T., & Nithya, S. (2014). A note on the zero divisor graph of a lattice. Transactions on Combinatorics, 3(3), 51-59. doi: 10.22108/toc.2014.5626
MLA
T. Tamizh Chelvam; S. Nithya. "A note on the zero divisor graph of a lattice". Transactions on Combinatorics, 3, 3, 2014, 51-59. doi: 10.22108/toc.2014.5626
HARVARD
Tamizh Chelvam, T., Nithya, S. (2014). 'A note on the zero divisor graph of a lattice', Transactions on Combinatorics, 3(3), pp. 51-59. doi: 10.22108/toc.2014.5626
VANCOUVER
Tamizh Chelvam, T., Nithya, S. A note on the zero divisor graph of a lattice. Transactions on Combinatorics, 2014; 3(3): 51-59. doi: 10.22108/toc.2014.5626
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