Work

An End Degree for Digraphs

Year: 2026

Type: article

Abstract: ABSTRACT In this paper we define a degree for ends of infinite digraphs. The well‐definedness of our definition in particular resolves a problem by Zuther. Furthermore, we extend our notion of end degree to also respect, among others, the vertices dominating the end, which we denote as combined end degree. Our main result is a characterisation of the combined end degree in terms of certain sequences of vertices, which we call end‐exhausting sequences. This establishes a similar, although more complex relationship as known for the combined end degree and end‐defining sequences in undirected graphs.

Source: Journal of Graph Theory

DOI: 10.1002/jgt.70084

Authors: Matthias Hamann, Karl Heuer

Institutions: Universität Hamburg, Technical University of Denmark

Language: English

Topic: Advanced Graph Theory Research

Subfield: Computational Theory and Mathematics

Field: Computer Science

Domain: Physical Sciences

Open Access status: hybrid

Estimated APC paid: $4,150

Funder: Deutsche Forschungsgemeinschaft