Geodetic Graphs: Experiments and New Constructions
Abstract
In 1962 Ore initiated the study of geodetic graphs. A graph is called geodetic if the shortest path between every pair of vertices is unique. In the subsequent years a wide range of papers appeared investigating their peculiar properties. Yet, a complete classification of geodetic graphs is out of reach. In this work we present a program enumerating all geodetic graphs of a given size. Using our program, we succeed to find all geodetic graphs with up to 25 vertices and all regular geodetic graphs with up to 32 vertices. This leads to the discovery of two new infinite families of geodetic graphs.
Cite
@article{arxiv.2308.08970,
title = {Geodetic Graphs: Experiments and New Constructions},
author = {Florian Stober and Armin Weiß},
journal= {arXiv preprint arXiv:2308.08970},
year = {2025}
}
Comments
The second version corrects an error in the first version, where we claimed that there are 32 biconnected geodetic graphs with 25 vertices. There are 33 such graphs