منابع مشابه
The Least Eigenvalue of Graphs
In this paper we investigate the least eigenvalue of a graph whose complement is connected, and present a lower bound for the least eigenvalue of such graph. We also characterize the unique graph whose least eigenvalue attains the second minimum among all graphs of fixed order.
متن کاملNotes on graphs with least eigenvalue at least -2
A new proof concerning the determinant of the adjacency matrix of the line graph of a tree is presented and an invariant for line graphs, introduced by Cvetković and Lepović, with least eigenvalue at least −2 is revisited and given a new equivalent definition [D. Cvetković and M. Lepović. Cospectral graphs with least eigenvalue at least −2. Publ. Inst. Math., Nouv. Sér., 78(92):51–63, 2005.]. E...
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We prove that for (Baire) almost every C’° periodic function V d2/dx2 + V has all its instability intervals non-empty. In the spectral theory of one dimensional Schrodinger operators [3] [10] with periodic potentials, a natural question occurs involving the presence of gaps in the spectrum. Let H = d2 2 + V on L2(R, d x) where V(x + 1) = V(x) for all x. Let AP (resp. AA) be the operator 2014201...
متن کاملGreatest Least Eigenvalue of the Laplacian on the Klein Bottle
We prove the following conjecture recently formulated by Jakobson, Nadirashvili and Polterovich [12]: For any Riemannian metric g on the Klein bottle K one has λ1(K, g)A(K, g) ≤ 12πE(2 √ 2/3), where λ1(K, g) and A(K, g) stand for the least positive eigenvalue of the Laplacian and the area of (K, g), respectively, and E is the complete elliptic integral of the second kind. Moreover, the equality...
متن کاملThe Chromatic Number and the Least Eigenvalue of a Graph
In this paper we get a structural property for a graph having the minimal least eigenvalue among all graphs of fixed order and given chromatic number, and characterize such graphs under the condition that the chromatic number is not larger than half the order of the graph. As a result, we obtain a lower bound on the least eigenvalue in terms of the chromatic number, and an upper bound on the ch...
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ژورنال
عنوان ژورنال: Journal d'Analyse Mathématique
سال: 1956
ISSN: 0021-7670,1565-8538
DOI: 10.1007/bf02937345