Mathematics

Research from China University provides new data about linear algebra

  2008 NOV 10 - (VerticalNews.com) -- According to recent research from Shandong, People's Republic of China, "The study of limit points of eigenvalues of adjacency matrices of graphs was initiated by Hoffman [A.J. Hoffman, On limit points of spectral radii of non-negative symmetric integral matrices, in: Y. Alavi et al. (Eds.), Lecture Notes Math., vol. 303, Springer-Verlag, Berlin, Heidelberg, New York, 1972, pp. 165-172]."

  "There he described all of the limit points of the largest eigenvalue of adjacency matrices of graphs that are no more than root 2 + root 5. In this paper, we investigate limit points of Laplacian spectral radii of graphs. The result is obtained: Let omega = 1/3 ((3)root 19 + 3 root 33 + (3)root 19 - 3 root 33+ 1), beta(0) = 1 and beta(n) (n >= 1) be the largest positive root of P-n(x) = x(n+1) - (1 + x + ... + x(n-1)) (root x + 1)(2). Let alpha(n) = 2 + beta(1/2)(n) + beta(-1/2)(n)," wrote J.M. Guo and colleagues, China University.

  The researchers concluded: "Then 4 = alpha(0) < alpha(1) < alpha(2) < ... are all of the limit points of Laplacian spectral radii of graphs smaller than lim(n ->) (infinity) alpha(n) = 2 + omega + omega(-1) (= 4.38+)."

  Guo and colleagues published their study in Linear Algebra and Its Applications (On limit points of Laplacian spectral radii of graphs. Linear Algebra and Its Applications, 2008;429(7):1705-1718).

  For additional information, contact J.M. Guo, China University Petr, Dept. of Applied Math, Dongying 257061, Shandong, People's Republic of China.

  Publisher contact information for the journal Linear Algebra and Its Applications is: Elsevier Science Inc., 360 Park Avenue South, New York, NY 10010-1710, USA.

  Keywords: Mathematics, China University.

  This article was prepared by VerticalNews Mathematics editors from staff and other reports. Copyright 2008, VerticalNews Mathematics via VerticalNews.com.