Reconstruction of small graphs and digraphs

TL;DR

This paper uses computer searches to verify the graph reconstruction conjecture for small graphs and digraphs, providing new evidence and methods for understanding reconstructibility in combinatorial structures.

Contribution

The paper presents computational proofs for the reconstruction conjecture for graphs up to 13 vertices and extends analysis to tournaments, digraphs, and posets, advancing the field's empirical knowledge.

Findings

Confirmed the conjecture for graphs with up to 13 vertices

Extended reconstructibility results to tournaments and digraphs

Provided computational methods for set reconstruction problems

Abstract

We describe computer searches that prove the graph reconstruction conjecture for graphs with up to 13 vertices and some limited classes on larger sizes. We also investigate the reconstructibility of tournaments up to 13 vertices, digraphs up to 9 vertices, and posets up to 13 points. In all cases, our results also apply to the set reconstruction problem that uses the isomorph-reduced deck.