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Can one hear the spanning trees of a quantum graph?
- Source :
-
Letters in Mathematical Physics . Apr2023, Vol. 113 Issue 2, p1-16. 16p. - Publication Year :
- 2023
-
Abstract
- Kirchhoff showed that the number of spanning trees of a graph is the spectral determinant of the combinatorial Laplacian divided by the number of vertices; we reframe this result in the quantum graph setting. We prove that the spectral determinant of the Laplace operator on a finite connected metric graph with standard (Neumann–Kirchhoff) vertex conditions determines the number of spanning trees when the lengths of the edges of the metric graph are sufficiently close together. To obtain this result, we analyze an equilateral quantum graph whose spectrum is closely related to spectra of discrete graph operators and then use the continuity of the spectral determinant under perturbations of the edge lengths. [ABSTRACT FROM AUTHOR]
Details
- Language :
- English
- ISSN :
- 03779017
- Volume :
- 113
- Issue :
- 2
- Database :
- Academic Search Index
- Journal :
- Letters in Mathematical Physics
- Publication Type :
- Academic Journal
- Accession number :
- 162404422
- Full Text :
- https://doi.org/10.1007/s11005-023-01656-0