$2$-Reconstructibility of Weakly Distance-Regular Graphs

TL;DR

This paper proves that strongly regular graphs with at least six vertices can be uniquely reconstructed from their subgraphs obtained by deleting two vertices, advancing understanding of graph reconstructibility.

Contribution

It establishes that strongly regular graphs with six or more vertices are 2-reconstructible, a new result in graph theory.

Findings

Strongly regular graphs with ≥6 vertices are 2-reconstructible.

The proof advances the theory of graph reconstructibility.

Provides a new criterion for reconstructing certain classes of graphs.

Abstract

A graph is $\ell$-reconstructible if it is determined by its multiset of induced subgraphs obtained by deleting $\ell$ vertices. We prove that strongly regular graphs with at least six vertices are $2$-reconstructible.