Kekul\'e Cells for Molecular Computation

TL;DR

This paper introduces Kekule9 cells, a graph-based model for molecular computation, analyzing their states and potential for switching behavior, with implications for molecular logic devices.

Contribution

It develops the theory of Kekule9 states and cells, classifies small cases, and explores their application as molecular switches and connectors.

Findings

Classified Kekule9 cells with up to 4 ports.

Generalized Kekule9 states to semi-Kekule9 states via linear systems.

Identified omniconjugated graphs as potential molecular connectors.

Abstract

The configurations of single and double bonds in polycyclic hydrocarbons are abstracted as Kekul\'e states of graphs. Sending a so-called soliton over an open channel between ports (external nodes) of the graph changes the Kekul\'e state and therewith the set of open channels in the graph. This switching behaviour is proposed as a basis for molecular computation. The proposal is highly speculative but may have tremendous impact. Kekul\'e states with the same boundary behaviour (port assignment) can be regarded as equivalent. This gives rise to the abstraction of Kekul\'e cells. The basic theory of Kekul\'e states and Kekul\'e cells is developed here, up to the classification of Kekul\'e cells with $\leq 4$ ports. To put the theory in context, we generalize Kekul\'e states to semi-Kekul\'e states, which form the solutions of a linear system of equations over the field of the bits 0 and 1. We briefly study so-called omniconjugated graphs, in which every port assignment of the right signature has a Kekul\'e state. Omniconjugated graphs may be useful as connectors between computational elements. We finally investigate some examples with potentially useful switching behaviour.