# Dispersion relations of periodic quantum graphs associated with Archimedean tilings (II)

## TL;DR

This paper derives explicit dispersion relations for quantum graphs related to five Archimedean tilings, expanding previous work and analyzing their spectral properties using symbolic computation.

## Contribution

It provides new dispersion relations for five additional Archimedean tilings, enhancing understanding of their spectral characteristics.

## Key findings

- Explicit dispersion relations derived for five Archimedean tilings.
- Spectral analysis performed using Mathematica.
- Enhanced understanding of the spectra of these quantum graphs.

## Abstract

We continue the work of a previous paper \cite{LJL} to derive the dispersion relations of the periodic quantum graphs associated with the remaining 5 of the 11 Archimedean tilings, namely the truncated hexagonal tiling $(3,12^2)$, rhombi-trihexagonal tiling $(3,4,6,4)$, snub square tiling $(3^2,4,3,6)$, snub trihexagonal tiling $(3^4,6)$, and truncated trihexagonal tiling $(4,6,12)$. The computation is done with the help of the symbolic software Mathematica. With these explicit dispersion relations, we perform more analysis on the spectra.