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Weak chain-completeness and fixed point property for pseudo-ordered sets

S. Parameshwara Bhatta (2005)

Czechoslovak Mathematical Journal

In this paper the notion of weak chain-completeness is introduced for pseudo-ordered sets as an extension of the notion of chain-completeness of posets (see [3]) and it is shown that every isotone map of a weakly chain-complete pseudo-ordered set into itself has a least fixed point.

When a line graph associated to annihilating-ideal graph of a lattice is planar or projective

Atossa Parsapour, Khadijeh Ahmad Javaheri (2018)

Czechoslovak Mathematical Journal

Let ( L , ∧ , ∨ ) be a finite lattice with a least element 0. 𝔸 G ( 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 ( 𝔸 G ( L ) ) , is a planar or projective graph.

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