---
tag: ATVXY7XAKE
kind: concept
name: Berlekamp–Van Lint–Seidel graph
sources:
  - wikipedia: en:59945606@r1360618382
    locator: Berlekamp–Van Lint–Seidel graph
    note: adopted
    mention: wikipedia://en/59945606
    sections: [Summary]
same_as:
  wikidata: Q61743750
  wikipedia: Berlekamp–Van Lint–Seidel graph
inventory: [PDYKVS3DR2]
---

## Summary

In graph theory, the **Berlekamp–Van Lint–Seidel graph** is a locally linear strongly regular graph with parameters $(243,22,1,2)$. This means that it has 243 vertices, 22 edges per vertex (for a total of 2673 edges), exactly one shared neighbor per pair of adjacent vertices, and exactly two shared neighbors per pair of non-adjacent vertices. It was constructed by Elwyn Berlekamp, J. H. van Lint, and Johan Jacob Seidel as the coset graph of the ternary Golay code.