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The Brouwer–Haemers graph is the first in an infinite family of Ramanujan graphs defined as generalized Paley graphs over fields of characteristic three. [2] With the 3 × 3 {\displaystyle 3\times 3} Rook's graph and the Games graph , it is one of only three possible strongly regular graphs whose parameters have the form ( ( n 2 + 3 n − 1 ...
Brouwer has confirmed by computation that the conjecture is valid for all graphs with at most 10 vertices. [1] It is also known that the conjecture is valid for any number of vertices if t = 1, 2, n − 1, and n. For certain types of graphs, Brouwer's conjecture is known to be valid for all t and for any number of vertices
The 1980 monograph Spectra of Graphs [16] by Cvetković, Doob, and Sachs summarised nearly all research to date in the area. In 1988 it was updated by the survey Recent Results in the Theory of Graph Spectra. [17] The 3rd edition of Spectra of Graphs (1995) contains a summary of the further recent contributions to the subject. [15]
The NFL playoffs are set. After a Week 18 that saw Tampa Bay and Denver claim the two remaining playoff spots, and multiple other teams lock in their seeding, the path to the Super Bowl finally ...
Andries Brouwer and Hendrik van Maldeghem (see #References) use an alternate but fully equivalent definition of a strongly regular graph based on spectral graph theory: a strongly regular graph is a finite regular graph that has exactly three eigenvalues, only one of which is equal to the degree k, of multiplicity 1.
America’s top investors have achieved double-digit returns for years, sometimes decades. Following these top investors is a great strategy for two reasons.
(The Center Square) – Seattle residents that utilize the city’s public pools, gyms and athletic centers will see fee increases next year to help offset salary increases. On Jan. 1, 2025 ...
The degree of a map between general manifolds was first defined by Brouwer, [1] who showed that the degree is homotopy invariant and used it to prove the Brouwer fixed point theorem. Less general forms of the concept existed before Brouwer, such as the winding number and the Kronecker characteristic (or Kronecker integral). [2]