RAMANUJAN POLAR GRAPHS

Document Type : Original Manuscript

Author

Dipartimento di Tecnica e Gestione dei Sistemi Industriali, Università degli Studi di Padova, Stradella S. Nicola 3, 36100, Vicenza, Italy.

10.22044/jas.2024.14231.1809

Abstract

Recently, a construction of minimal codes arising from a family of almost Ramanujan graphs was shown. Ramanujan graphs are examples of expander graphs that minimize the second-largest eigenvalue of their adjacency matrix. We call such graphs Ramanujan, since all known non-trivial constructions imply the Ramanujan conjecture on arithmetical functions. In this paper, we prove that some families of tangent graphs of finite classical polar spaces satisfy Ramanujan's condition. If the polarity is unitary, or it is orthogonal and the quadric is over the binary field, the tangent graphs are strongly regular, and we know their spectrum. By direct computation, it is possible to show which families of tangent graphs are Ramanujan.

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References

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Journal of Algebraic Systems
Volume 14, Issue 2
April 2026
Pages 271-280

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