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...

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...

reinterpreted graph-theoretically. It was Toshikazu Sunada who put this suggestion into practice in 1985. As observed by Sunada, a regular graph is a Ramanujan graph...

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...

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...

theta function Ramanujan graph Ramanujan's tau function Ramanujan's ternary quadratic form Ramanujan prime Ramanujan's constant Ramanujan's lost notebook...

the two-by-two p-adic special linear group. A regular finite graph is a Ramanujan graph, a mathematical model of efficient communication networks, if...

Miguel A (2006-08-07). "Optimal network topologies: expanders, cages, Ramanujan graphs, entangled networks and all that". Journal of Statistical Mechanics:...

In graph theory, a graph is said to be a pseudorandom graph if it obeys certain properties that random graphs obey with high probability. There is no concrete...

theory to construct efficient communication networks called Ramanujan graphs and Ramanujan complexes. Li did her undergraduate studies at National Taiwan...

can be used to construct expander graphs (Margulis), or even Ramanujan graphs (Lubotzky-Phillips-Sarnak). Such graphs are known to exist in abundance by...

Srinivasa Ramanujan first discovered that the partition function has nontrivial patterns in modular arithmetic, now known as Ramanujan's congruences...

solving long-standing questions on the Kadison-Singer problem and on Ramanujan graphs.[1] In 2022 The Ciprian Foias Prize in Operator Theory was awarded...

eigenvector. The graphs that come close to meeting this bound are Ramanujan graphs, which are examples of the best possible expander graphs. Its discoverers...

(1988), "Ramanujan graphs", Combinatorica, 8 (3): 261–277, doi:10.1007/BF02126799, MR 0963118. Tutte, W. T. (1947), "A family of cubical graphs", Proc....

(with A. Lubotzky and R. Phillips) applied results in number theory to Ramanujan graphs, with connections to combinatorics and computer science. Sarnak has...

2021 for their solution to long-standing conjectures in the study of Ramanujan graphs. Marcus grew up in Marietta, Georgia and was a boarding student at...

gave the first construction of expander graphs, which was later generalized in the theory of Ramanujan graphs. In 1986, Margulis gave a complete resolution...

combinatorics, algebraic, differential, discrete and Euclidean geometries, graph theory, group theory, model theory, number theory, set theory, Ramsey theory...

regular bipartite graphs with arbitrarily large number of vertices such that each graph G {\displaystyle G} in the sequence is a Ramanujan graph. It is called...

Ramanujan prime, Ramanujan summation, Ramanujan graph and Ramanujan's sum – Discovered by the Indian mathematician Srinivasa Ramanujan in the early 20th...

Ramanujan Institute for Advanced Study in Mathematics (RIASM) is the Department of Mathematics of University of Madras. This name was adopted in 1967...

Daniel; Mouawad, Amer E.; Panolan, Fahad; Ramanujan, M. S.; Saurabh, Saket (2015), "Reconfiguration on sparse graphs", in Dehne, Frank; Sack, Jörg-Rüdiger;...

A.; Srivastava, Nikhil (2015), "Interlacing families I: Bipartite Ramanujan graphs of all degrees", Annals of Mathematics, 182 (1): 307–325, arXiv:1304...