When a line graph associated to annihilating-ideal graph of a lattice is planar or projective |
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Authors: | Atossa Parsapour Khadijeh Ahmad Javaheri |
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Institution: | 1.Department of Mathematics,Bandar Abbas Branch, Islamic Azad University,Bandar Abbas,Iran |
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Abstract: | Let (L,∧, ∨) be a finite lattice with a least element 0. AG(L) is an annihilating-ideal graph of L in which the vertex set is the set of all nontrivial ideals of L, and two distinct vertices I and J are adjacent if and only if I ∧ J = 0. We completely characterize all finite lattices L whose line graph associated to an annihilating-ideal graph, denoted by L(AG(L)), is a planar or projective graph. |
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