Given a graph G with vertex set V (G) = V and edge set E(G) = E, let Gl be the line graph and Gc the complement of G. Let G0 be the graph with V (G0) = V and with no edges, G1 the complete graph with the vertex set V , G+ = G and G− = Gc. Let B(G) (Bc(G)) be the graph with the vertex set V ∪E and such that (v, e) is an edge in B(G) (resp., in Bc(G)) if and only if v ∈ V , e ∈ E and vertex v is ...

1. Introduction We deene the notion of a loop and use it to derive properties of non

We introduce a definition of admissibility for subintervals in interval exchange transformations. Using this notion, we prove a property of the natural codings of interval exchange transformations, namely that any derived set of a regular interval exchange set is a regular interval exchange set with the same number of intervals. Derivation is taken here with respect to return words. We characte...