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...

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

constructions to produce Ramanujan graphs with a fixed vertex size and degree of regularity. The results show the Ramanujan graphs exist for every vertex...

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...

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

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...

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...

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...

2{\sqrt {d-1}}-o(1)} . This bound is tight in the Ramanujan graphs. Suppose two directed or undirected graphs G1 and G2 with adjacency matrices A1 and A2 are...

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

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

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...

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

machine Ramanujan–Nagell equation Ramanujan–Peterssen conjecture Ramanujan–Soldner constant Ramanujan summation Ramanujan theta function Ramanujan graph Ramanujan's...

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

Thiruvenkatachari Parthasarathy. Ramanujan theta function, Ramanujan prime, Ramanujan summation, Ramanujan graph and Ramanujan's sum – Discovered by the Indian...

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

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

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

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

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

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...

of Integer Quaternions". Elementary Number Theory, Group Theory and Ramanujan Graphs. London Mathematical Society Student Texts. Vol. 55. Cambridge University...

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

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...

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

In graph theory, an odd cycle transversal of an undirected graph is a set of vertices of the graph that has a nonempty intersection with every odd cycle...