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...

In mathematics, the Ramanujan conjecture, due to Srinivasa Ramanujan (1916, p. 176), states that Ramanujan's tau function given by the Fourier coefficients...

mathematicians List of Indian mathematicians Ramanujan graph Ramanujan summation Ramanujan's constant Ramanujan's ternary quadratic form Rank of a partition...

<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 |...

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...

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...

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...

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...

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...

This bound is tight in the Ramanujan graphs, which have applications in many areas. Suppose two directed or undirected graphs G1 and G2 with adjacency matrices...