Graph isomorphism of ordered sets

Rok, strany: 2002, 491 - 499

Two discrete (semi)lattices having isomorphic graphs, are compatible (semi)lattice orders of each other if and only if all their sub(semi)lattices of certain types are preserved or reversed. In the paper, we show that all connected compatible orderings of a lattice have graphs isomorphic to the graph of the lattice; and then we characterize all compatible orderings of a lattice in term of subgraphs of the lattice. It turns out that the consideration of certain types of sublattices of a lattice $L$ leads to necessary and sufficient conditions for all ordered sets whose graphs are isomorphic to $L$ to be compatible orderings of $L$. The results cover all the cases of compatible lattice orderings.

ISO 690:

Ratanaprasert, C. 2002. Graph isomorphism of ordered sets. In Mathematica Slovaca, vol. 52, no.5, pp. 491-499. 0139-9918.

APA:

Ratanaprasert, C. (2002). Graph isomorphism of ordered sets. Mathematica Slovaca, 52(5), 491-499. 0139-9918.