Resonantly Equivalent Catacondensed Even Ring Systems

TL;DR

This paper extends binary coding of perfect matchings to catacondensed even ring systems, introduces resonantly equivalent cers, and explores conditions for resonance graph isomorphism with benzenoid graphs, revealing structural correspondences.

Contribution

It generalizes coding procedures and introduces the concept of resonantly equivalent cers, linking their resonance graphs to those of benzenoid graphs.

Findings

Resonantly equivalent cers have isomorphic resonance graphs.

For each phenylene, a corresponding catacondensed benzenoid graph exists with an isomorphic resonance graph.

The paper establishes structural conditions for resonance graph isomorphism.

Abstract

In this paper we generalize the binary coding procedure of perfect matchings from catacondensed benzenoid graphs to catacondensed even ring systems (also called cers). Next, we study cers with isomorphic resonance graphs. For this purpose, we define resonantly equivalent cers. Finally, we investigate cers whose resonance graphs are isomorphic to the resonance graphs of catacondensed benzenoid graphs. As a consequence we show that for each phenylene there exists a catacondensed benzenoid graph such that their resonance graphs are isomorphic.