Geodesic
Estimate of the First Eigenvalue of the Laplacian on a Graph
Matematičeskie zametki, Tome 96 (2014) no. 6, pp. 885-895

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The eigenvalue problem for the Laplacian with Dirichlet boundary conditions on a graph is considered. The main result is an estimate of the first (minimal) eigenvalue. The proof is based on the Schwartz symmetrization of a function on a graph and on its properties.
Keywords: eigenvalue problem, Schwartz symmetrization, Laplacian on a graph. 
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     author = {A. T. Diab and P. A. Kuleshov and O. M. Penkin},
     title = {Estimate of the {First} {Eigenvalue} of the {Laplacian} on a {Graph}},
     journal = {Matemati\v{c}eskie zametki},
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     url = {http://geodesic.mathdoc.fr/item/MZM_2014_96_6_a7/}
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A. T. Diab; P. A. Kuleshov; O. M. Penkin. Estimate of the First Eigenvalue of the Laplacian on a Graph. Matematičeskie zametki, Tome 96 (2014) no. 6, pp. 885-895. http://geodesic.mathdoc.fr/item/MZM_2014_96_6_a7/