2021
DOI: 10.1038/s41598-021-94331-0
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A new spectral invariant for quantum graphs

Abstract: The Euler characteristic i.e., the difference between the number of vertices |V| and edges |E| is the most important topological characteristic of a graph. However, to describe spectral properties of differential equations with mixed Dirichlet and Neumann vertex conditions it is necessary to introduce a new spectral invariant, the generalized Euler characteristic $$\chi _G:= |V|-|V_D|-|E|$$ χ G … Show more

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Cited by 13 publications
(12 citation statements)
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“…In Refs. [21,22], the formulas for the Euler characteristic for graphs with the standard boundary conditions at the vertices and with the mixed ones, standard and Dirichlet boundary conditions at vertices, were derived. In the case of the standard boundary conditions,…”
Section: The Generalized Euler Characteristicmentioning
confidence: 99%
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“…In Refs. [21,22], the formulas for the Euler characteristic for graphs with the standard boundary conditions at the vertices and with the mixed ones, standard and Dirichlet boundary conditions at vertices, were derived. In the case of the standard boundary conditions,…”
Section: The Generalized Euler Characteristicmentioning
confidence: 99%
“…From the experimental point of view, the usefulness of Equation ( 6) stems from the fact that the generalized Euler characteristic can be evaluated using only a limited number K = K min of the lowest eigenvalues (resonances) [21,22,68,69]…”
Section: The Generalized Euler Characteristicmentioning
confidence: 99%
See 3 more Smart Citations