Journal article

On The Abstract Properties Of Markov Graphs For Maps On Trees

Year:

2017

Published in:

Matematicki Bilten
dynamical system
Markov graph
isomorphism classes
M-graphs
tournaments

Having a dynamical system on the vertex set of a finite tree, one can construct the corresponding Markov graph which is the digraph that encodes covering relation between edges in a tree. Representatives of isomorphism classes of Markov graphs are called M-graphs. In this paper we prove that the class of M-graphs is closed under several prescribed digraph transformations (such as deletion of a vertex in a digraph or taking the disjoint union of digraphs, for example). We also give a complete list of tournaments which are M-graphs as well as of M-graphs with three vertices.

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