AN UPPER BOUND ON THE DIAMETER OF A GRAPH FROM EIGENVALUES ASSOCIATEDWITH ITS LAPLACIAN

Authors
CHUNG FRK FABER V MANTEUFFEL TA
Citation
Frk. Chung et al., AN UPPER BOUND ON THE DIAMETER OF A GRAPH FROM EIGENVALUES ASSOCIATEDWITH ITS LAPLACIAN, SIAM journal on discrete mathematics, 7(3), 1994, pp. 443-457
Citations number
17
Categorie Soggetti
Mathematics,Mathematics
Journal title
SIAM journal on discrete mathematics → ACNP
ISSN journal
08954801
Volume
7
Issue
3
Year of publication
1994
Pages
443 - 457
Database
ISI
SICI code
0895-4801(1994)7:3<443:AUBOTD>2.0.ZU;2-6
Abstract
The authors give a new upper bound for the diameter D(G) of a graph G in terms of the eigenvalues of the Laplacian of G. The bound is D(G) l ess-than-or-equal-to [cosh-1 (n - 1)/cosh-1 (lambda(n) + lambda2/lambd a(n) - lambda2)] + 1. where 0 less-than-or-equal-to lambda2 less-than- or-equal-to ... less-than-or-equal-to lambda(n) are the eigenvalues of the Laplacian of G and where [] is the floor function.