Classification of some countable descendant-homogeneous digraphs

TL;DR

This paper classifies certain countable descendant-homogeneous digraphs with q-valent tree descendant sets and provides conditions for constructing such digraphs with specified descendant structures.

Contribution

It offers a complete classification for finite q and introduces conditions to construct digraphs with prescribed descendant set structures.

Findings

Classified all countable descendant-homogeneous digraphs with q-valent tree descendant sets for finite q.

Established conditions for constructing digraphs with specific descendant set isomorphisms.

Extended understanding of the structure and construction of descendant-homogeneous digraphs.

Abstract

For finite q, we classify the countable, descendant-homogeneous digraphs in which the descendant set of any vertex is a q-valent tree. We also give conditions on a rooted digraph G which allow us to construct a countable descendant-homogeneous digraph in which the descendant set of any vertex is isomorphic to G.