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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
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References:
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