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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]
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.
Philippe J.S. De Brouwer (born 21 February 1969) is a European investment and banking professional as well as academician in finance and investing. As a scientist he is mostly known for his solution to the Fallacy of Large Numbers (formulated by Paul A Samuelson in 1963) and his formulation of the Maslowian Portfolio Theory in the field of investment advice (and annex theory Target Oriented ...
By the closed graph theorem, is in the spectrum if and only if the bounded operator : is non-bijective on . The study of spectra and related properties is known as spectral theory , which has numerous applications, most notably the mathematical formulation of quantum mechanics .
In mathematics, the energy of a graph is the sum of the absolute values of the eigenvalues of the adjacency matrix of the graph. This quantity is studied in the context of spectral graph theory. More precisely, let G be a graph with n vertices. It is assumed that G is a simple graph, that is, it does not
A cubic graph (all vertices have degree three) of girth g that is as small as possible is known as a g-cage (or as a (3,g)-cage).The Petersen graph is the unique 5-cage (it is the smallest cubic graph of girth 5), the Heawood graph is the unique 6-cage, the McGee graph is the unique 7-cage and the Tutte eight cage is the unique 8-cage. [3]