On disjoint union of M-graphs

Abstract

Given a pair (X,σ) consisting of a finite tree X and its vertex self-map σ one can construct the corresponding Markov graph Γ(X,σ) which is a digraph that encodes σ-covering relation between edges in X. M-graphs are Markov graphs up to isomorphism. We obtain several sufficient conditions for the disjoint union of M-graphs to be an M-graph and prove that each weak component of M-graph is an M-graph itself.