Shahrood University of Technology Journal of Algebraic Systems 2345-5128 14 2 2026 04 01 RAMANUJAN POLAR GRAPHS 271 280 3736 10.22044/jas.2024.14231.1809 EN Valentino Smaldore Dipartimento di Tecnica e Gestione dei Sistemi Industriali, Università degli Studi di Padova, Stradella S. Nicola 3, 36100, Vicenza, Italy. 0000-0003-3433-3164 Journal Article 2024 02 24 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. https://jas.shahroodut.ac.ir/article_3736_4b4dac96d79fabe7c1de11412e72276f.pdf