Year: 2022
Type: preprint
Abstract: We consider a dual Cheeger constant $\overline h$ for finite graphs with edge weights from an arbitrary real-closed ordered field. We obtain estimates of $\overline h$ in terms of number of vertices in graph. Further, we estimate the largest eigenvalue for the discrete Laplace operator in terms of $\overline h$ and show the sharpness of estimates. As an example we consider graphs over non-Archimedean field of the Levi-Civita numbers.
Source: arXiv (Cornell University)
Author: Muranova, Anna
Institution: University of Warmia and Mazury in Olsztyn
Language: English
Subfield: Mathematical Physics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W4308243578