spectral graph theory, a Ramanujan graph is a regular graph whose spectral gap is almost as large as possible (see extremal graph theory). Such graphs are...
19 KB (2,689 words) - 01:42, 4 January 2024
In mathematics, the Ramanujan conjecture, due to Srinivasa Ramanujan (1916, p. 176), states that Ramanujan's tau function given by the Fourier coefficients...
19 KB (2,424 words) - 12:07, 14 May 2024
mathematicians List of Indian mathematicians Ramanujan graph Ramanujan summation Ramanujan's constant Ramanujan's ternary quadratic form Rank of a partition...
101 KB (10,989 words) - 17:17, 2 July 2024
Theory, Group Theory and Ramanujan Graphs is a book in mathematics whose goal is to make the construction of Ramanujan graphs accessible to undergraduate-level...
8 KB (1,023 words) - 04:10, 11 December 2023
<2{\sqrt {d-1}}} , there are only finitely many (n, d, λ)-graphs. Ramanujan graphs are d-regular graphs for which this bound is tight, satisfying λ = max |...
38 KB (5,147 words) - 10:56, 25 June 2024
to be Ramanujan graphs, graphs with optimal expansion properties for their degree. The proof is based on Pierre Deligne's proof of the Ramanujan–Petersson...
6 KB (649 words) - 08:25, 18 June 2023
arrows. radius The radius of a graph is the minimum eccentricity of any vertex. Ramanujan A Ramanujan graph is a graph whose spectral expansion is as...
106 KB (15,667 words) - 12:01, 16 May 2024
finite fields. These remarkable Ramanujan graphs also have large expansion coefficient. The odd girth and even girth of a graph are the lengths of a shortest...
7 KB (903 words) - 09:27, 5 June 2024
Alon–Boppana bound (category Algebraic graph theory)
eigenvector. The graphs that come close to meeting this bound are Ramanujan graphs, which are examples of the best possible expander graphs. Its discoverers...
9 KB (1,908 words) - 16:59, 7 February 2024
edges. It is a strongly regular graph, a distance-transitive graph, and a Ramanujan graph. Although its construction is folklore, it was named after Andries...
6 KB (714 words) - 00:30, 19 August 2023