Dual Cheeger constant for weighted graphs over ordered fields

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.

arXiv comment14 pages, 1 figure