Christophe Texier 2008 J. Phys. A: Math. Theor. 41 085207 doi:10.1088/1751-8113/41/8/085207
On the spectrum of the Laplace operator of metric graphs attached at a vertex—spectral determinant approach
Christophe Texier
Show affiliationsWe consider a metric graph 
made of two graphs 
and 
attached at one point. We derive a formula relating the spectral determinant of the Laplace operator 
in terms of the spectral determinants of the two subgraphs. The result is generalized to describe the attachment of n graphs. The formulae are also valid for the spectral determinant of the Schrödinger operator 
.
- PACS
- MSC
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05Cxx Graph theory (For applications of graphs, see 68R10, 90C35, 94C15)
- Subjects
- Dates
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Issue 8 (29 February 2008)
Received 1 June 2007, in final form 20 December 2007
Published 12 February 2008
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On the spectrum of the Laplace operator of metric graphs attached at a vertex—spectral determinant approach
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