# Resonance graphs of catacondensed even ring systems

## TL;DR

This paper studies the resonance graphs of catacondensed even ring systems, characterizing when they are daisy cubes and establishing isomorphism conditions for even ring chains.

## Contribution

It provides a characterization of CERS resonance graphs as daisy cubes and generalizes known results from kinky benzenoid graphs.

## Key findings

- Two even ring chains are resonantly equivalent iff their resonance graphs are isomorphic.
- Characterization of CERS with resonance graphs as daisy cubes.
- Extension of results from kinky benzenoid graphs to CERS.

## Abstract

A catacondensed even ring system (shortly CERS) is a simple bipartite 2-connected outerplanar graph with all vertices of degree 2 or 3. In this paper, we investigate the resonance graphs (also called $Z$-transformation graphs) of CERS and firstly show that two even ring chains are resonantly equivalent iff their resonance graphs are isomorphic. As the main result, we characterize CERS whose resonance graphs are daisy cubes. In this way, we greatly generalize the result known for kinky benzenoid graphs. Finally, some open problems are also presented.