More on linear and metric tree maps

Opuscula Mathematica

article

Sergiy Kozerenko¹ 

[1] National University of Kyiv-Mohyla Academy, Department of Mathematics, Faculty of Informatics

关键词: tree;    Markov graph;    metric map;    non-expanding map;    linear map;    graph homomorphism.;   

DOI  :  10.7494/OpMath.2021.41.1.55

学科分类：环境科学（综合）

来源: AGH University of Science and Technology Press

【 摘 要 】

We consider linear and metric self-maps on vertex sets of finite combinatorial trees. Linear maps are maps which preserve intervals between pairs of vertices whereas metric maps are maps which do not increase distances between pairs of vertices. We obtain criteria for a given linear or a metric map to be a positive (negative) under some orientation of the edges in a tree, we characterize trees which admit maps with Markov graphs being paths and prove that the converse of any partial functional digraph is isomorphic to a Markov graph for some suitable map on a tree.

【 授权许可】

CC BY-NC