English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Plus annual

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Tools annual

Global: Zendy Free Plan

Global: Zendy Tools monthly

Global: Zendy Plus monthly

We consider a metric graph $\mathcal{G}$ made of two graphs $\mathcal{G}_1$and $\mathcal{G}_2$ attached at one point. We derive a formula relating thespectral determinant of the Laplace operator$S_\mathcal{G}(\gamma)=\det(\gamma-\Delta)$ in terms of the spectraldeterminants of the two subgraphs. The result is generalized to describe theattachment of $n$ graphs. The formulae are also valid for the spectraldeterminant of the Schr\"odinger operator $\det(\gamma-\Delta+V(x))$.

On the spectrum of the Laplace operator of metric graphs attached at a vertex -- Spectral determinant approach