Farey Series and Maximal Outerplanar Graphs
Charles J. Colbourn · SIAM Journal on Algebraic and Discrete Methods · 1982
Certain graphs representing Farey series of irreducible fractions are shown to be maximal outerplanar. For a suitable generalization of Farey series, the class of graphs obtained is exactly the class of maximal outerplanar graphs. Using a representation of maximal outerplanar graphs as series of irreducible fractions, efficient algorithms for deciding isomorphism of maximal outerplanar graphs and for deciding whether one maximal outerplanar graph is a subgraph of another are described.