Dual Cheeger constant for weighted graphs over ordered fields
- Resource Type
- Working Paper
- Authors
- Muranova, Anna
- Source
- Subject
- Mathematics - Combinatorics
Mathematics - Spectral Theory
05C50, 05C22, 47A75, 12J15, 39A12
- Language
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.
Comment: 14 pages, 1 figure