A Note on the Zero Divisor Graph of a Lattice T. Tamizh Chelvam∗ and S. Nithya
نویسنده
چکیده
Let L be a lattice with the least element 0. An element x ∈ L is a zero divisor if x∧ y = 0 for some y ∈ L∗ = L \ {0}. The set of all zero divisors is denoted by Z(L). We associate a simple graph Γ(L) to L with vertex set Z(L)∗ = Z(L) \ {0}, the set of non-zero zero divisors of L and distinct x, y ∈ Z(L)∗ are adjacent if and only if x ∧ y = 0. In this paper, we obtain certain properties and diameter and girth of the zero divisor graph Γ(L). Also we find a dominating set and the domination number of the zero divisor graph Γ(L).
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