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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 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 ...
The NFL playoff picture will soon be locked in, but teams still have an opening to make a statement. Here are our bold predictions for Week 17.
Ex-NYPD Commissioner Bill Bratton says the city needs more cops to crack down on subway mayhem and other crime, noting there were thousands more officers when he was first in charge in the 1990s.
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.
We finally—finally—made it to the end of the year.And though the music releases have gone from summer’s deluge to a steady trickle, that doesn’t mean there aren’t some great new songs in ...
For a graph G, let χ(G) denote the chromatic number and Δ(G) the maximum degree of G.The list coloring number ch(G) satisfies the following properties.. ch(G) ≥ χ(G).A k-list-colorable graph must in particular have a list coloring when every vertex is assigned the same list of k colors, which corresponds to a usual k-coloring.