A C.A.S. treatment of optimal-diameter double-loop digraphs families

A double-loop digraph (DLN) G(N;s1, s2) = G(V, E) is defined by V = ZN and E = {(i, i+s1), (i, i+s2) ⫫ i ϵ V}, for some fixed steps 1 ≤ s1 < s2 < N with gcd(N, s1, s2) = 1. Let D(N;s1, s2) be the diameter of G. L-shaped plane tiles have been used to modelize such digraphs, mainly for metrical-related properties. Some related known problems are:• xed N, s1 and s2 find D(N; s1, s2). xed N, find D(N) = min1≤s1<s2<N D(N; s1, s2). nd optimal diameter families of DLNs. P2 belong to numerical type problems and efficient algorithms to solve them are known. P3 is a problem of symbolic nature, so it can be studied with a Computer Algebra System. Some results on the latter problem will be treated in this paper, using the L-shaped tilesʹ approach.