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Double covers and logics of graphs. (English) Zbl 0537.05070
If $$A\subseteq VG$$ then $$A^{\perp}$$ is the set of all vertices of G which are adjacent to all vertices of A. In this paper, property P says for each $$x\in VG$$, and for each subset Y of VG, the equality $$x^{\perp}=Y^{\perp}$$ implies $$x\in Y$$. The logic, $${\mathcal L}(G)$$ of a graph G is a lattice derived from the operation $$A\mapsto A^{\perp}.$$ This paper proves results such as ”To each graph G there exist infinitely many graphs G’ without the property P, such that $${\mathcal L}(G)\cong {\mathcal L}(G')''.$$
Reviewer: D.A.Holton

##### MSC:
 05C99 Graph theory 06B99 Lattices
##### Keywords:
logics; double covers; neighborhood
Full Text:
##### References:
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