On inverse topology problem for Laplace operators on graphs

Authors

  • Yu.Yu. Ershova Institute of Mathematics, National Academy of Sciences of Ukraine, 3 Tereschenkivska str., 01601, Kyiv, Ukraine
  • I.I. Karpenko Vernadsky Taurida National University, 4 Vernadsky avenue, 95007, Simferopol, Ukraine
  • A.V. Kiselev Institute for Applied Problems of Mechanics and Mathematics, 3b Naukova str., 79060, Lviv, Ukraine
https://doi.org/10.15330/cmp.6.2.230-236

Keywords:

quantum graphs, Schrodinger operator, Laplace operator, inverse spectral problem, boundary triples, isospectral graphs
Published online: 2014-12-25

Abstract

Laplacian operators on finite compact metric graphs are considered under the assumption that matching conditions at graph vertices are of $\delta$ type. Under one additional assumption, the inverse topology problem is treated. Using the apparatus of boundary triples, we generalize and extend existing results on necessary conditions of isospectrality of two Laplacians defined on different graphs. A result is also given covering the case of Schrodinger operators.

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Ershova, Y.; Karpenko, I.; Kiselev, A. On Inverse Topology Problem for Laplace Operators on Graphs. Carpathian Math. Publ. 2014, 6, 230-236.