  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.
