quasi wrote: > >For P,Q in R^2, let |P - Q| denote the usual Euclidean distance >from P to Q. > >Define a graph G with vertex set Z^2 such that, for distinct >points P,Q in Z^2, PQ is an edge iff > > (1) |P - Q| is a positive integer. > > (2) The line segment PQ is not horizontal or vertical. > >For P,Q in Z^2, let d(P,Q) denote the graph-theoretic distance >from P to Q in the graph G. > >I'll pose 3 problems ... > >Problem (1) is fairly easy. > >Problem (2) is medium hard. > >For problem (3), I don't yet have a solution. > >(1) Show that G is connected. > >(2) Find points P,Q in Z^2 such that d(P,Q) = 3. > >(3) Prove or disprove: The diameter of G is 3.