The Electronic Journal of Combinatorics· 2026Q1
Geodetic Graphs: Experiments and New Constructions
- 0citations
- Q1SCImago
- 2026year
Short summary
A new algorithm enumerates biconnected geodetic graphs, discovering all such graphs up to 25 vertices and a new infinite family.
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Key points
- Developed an exhaustive search algorithm for enumerating biconnected geodetic graphs.
- Found all geodetic graphs with up to 25 vertices.
- Discovered a new infinite family of geodetic graphs.
- Presented a new method for constructing geodetic subdivisions of geodetic graphs.
AI-generated from the title and abstract; the full text is not read.
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 has appeared investigating their peculiar properties. Yet, a complete classification of geodetic graphs remains out of reach. In this work we present an exhaustive search algorithm for enumerating all biconnected geodetic graphs of a given order. Using our program, we 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 a new infinite family of geodetic graphs. Moreover, we present a new result on constructing geodetic subdivisions of geodetic graphs.
The authors' abstract, as published at the source. The Electronic Journal of Combinatorics, 2026 · DOI ↗
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Field: Computer Graphics and Computer-Aided Design
Computer Graphics and Computer-Aided DesignComputer Science