Optimization of eigenvalue bounds for the independence and chromatic number of graph powers
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DOI: 10.1016/j.disc.2021.112706
Abstract: The $k^{\text{th}}$ power of a graph $G=(V,E)$, $G^k$, is the graph whose vertex set is $V$ and in which two distinct vertices are adjacent if and only if their distance in $G$ is at most… read more here.
Keywords: eigenvalue bounds; graph; number; chromatic number ... See more keywords
A note on eigenvalue bounds for Schrödinger operators
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DOI: 10.1016/j.jmaa.2018.10.006
Abstract: We obtain a new bound on the location of eigenvalues for a non-self-adjoint Schr\"odinger operator with complex-valued potentials by obtaining a weighted $L^2$ estimate for the resolvent of the Laplacian. read more here.
Keywords: schr dinger; bounds schr; dinger operators; eigenvalue bounds ... See more keywords
Eigenvalue bounds for Stark operators with complex potentials
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DOI: 10.1090/tran/7873
Abstract: We consider the three-dimensional Stark operator perturbed by a complex-valued potential. We obtain an estimate for the number of eigenvalues of this operator as well as for the sum of imaginary parts of eigenvalues situated… read more here.
Keywords: operators complex; eigenvalue bounds; complex potentials; bounds stark ... See more keywords
Eigenvalue Bounds for a Class of Schrödinger Operators in a Strip
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DOI: 10.1155/2018/7172356
Abstract: This paper is concerned with the estimation of the number of negative eigenvalues (bound states) of Schrödinger operators in a strip subject to Neumann boundary conditions. The estimates involve weighted L1 norms and LlnL norms… read more here.
Keywords: eigenvalue bounds; dinger operators; bounds class; operators strip ... See more keywords