The general position number of digraphs

TL;DR

This paper studies the general position number in directed graphs, providing bounds, complexity results, and analysis for specific digraph families, extending the concept from undirected graphs.

Contribution

It introduces bounds, NP-completeness, and specific analyses for important digraph families, advancing understanding of the general position number in directed graphs.

Findings

Bounds for the general position number of digraphs

NP-completeness for oriented graphs

Analysis of circulant, Kautz, and permutation digraphs

Abstract

The general position number for graphs ask for largest vertex subsets $S$ such that no three vertices are contained on a common shortest path. We examine this problem in the setting of directed graphs. We provide bounds for the general position number of digraphs, show that the problem is NP-complete for oriented graphs, investigate the problem for some important families of digraphs such as circulant digraphs, Kautz digraphs and permutation digraphs, and study the general position numbers obtained from all orientations of an undirected graph.