منابع مشابه
Diameters and Eigenvalues
We derive a new upper bound for the diameter of a k-regular graphG as a function of the eigenvalues of the adjacency matrix. Namely, supposethe adjacency matrix of G has eigenvalues AI , A2 .••.• An with lAd:::: IA21 ::::... :::: IAnl where AI = k, A = IA21. Then the diameter D(G) must satisfy D(G) :::; rlog(n 1)f1og(k/A)l. We wilJ consider families of graphs whose eigenvalues can b...
متن کاملDiameters, distortion, and eigenvalues
We study the relation between the diameter, the first positive eigenvalue of the discrete p-Laplacian and the `p-distortion of a finite graph. We prove an inequality relating these three quantities and apply it to families of Cayley and Schreier graphs. We also show that the `p-distortion of Pascal graphs, approximating the Sierpinski gasket, is bounded, which allows to obtain estimates for the...
متن کاملGraphs with few distinct distance eigenvalues irrespective of the diameters
The distance matrix of a simple connected graph G is D(G) = (dij), where dij is the distance between ith and jth vertices of G. The multiset of all eigenvalues of D(G) is known as the distance spectrum of G. Lin et al.(On the distance spectrum of graphs. Linear Algebra Appl., 439:1662-1669, 2013) asked for existence of graphs other than strongly regular graphs and some complete k-partite graphs...
متن کاملOphthalmoscopic-Perspectively Distorted Optic Disc Diameters and Real Disc Diameters.
PURPOSE To investigate the difference between two-dimensionally measured disc diameters (DDs) based on fundus images and three-dimensionally measured DDs based on enhanced depth imaging optical coherence tomography (EDI-OCT). METHODS The DDs were three-dimensionally measured on EDI-OCT images of optic nerve heads and two-dimensionally measured on near-infrared reflectance fundus images in 90 ...
متن کاملA mathematically simple method based on denition for computing eigenvalues, generalized eigenvalues and quadratic eigenvalues of matrices
In this paper, a fundamentally new method, based on the denition, is introduced for numerical computation of eigenvalues, generalized eigenvalues and quadratic eigenvalues of matrices. Some examples are provided to show the accuracy and reliability of the proposed method. It is shown that the proposed method gives other sequences than that of existing methods but they still are convergent to th...
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ژورنال
عنوان ژورنال: Journal of the American Mathematical Society
سال: 1989
ISSN: 0894-0347
DOI: 10.2307/1990973