the assumption we have to make on our algebra. With this assumption, we can rewrite the action of the cellular chains as “operadic correlation functions” for decorated trees. In this description the operation of the chains of the framed little discs operad becomes apparent.

The results and techniques we present below can also be employed in other situations, which we comment on at the end of the paper. Notably one can use it to obtain an action of cells of a ribbon graph cell decomposition of moduli space on cyclic complexes. This should ultimately lead to string topology like operations of the cells of moduli space of decorated bordered surfaces on the free loop space of a compact manifold extending the operations of the string PROP or dioperad. The basic constructions for this are announced below.

Acknowledgments {#acknowledgments .unnumbered}
===============

We would like to thank Alain Connes for an enlightening discussion and Jim Stasheff for his valuable comments. We also thank the Max–Planck–Institute for Mathematics in Bonn for providing the atmosphere and stimulus to conceptualize and complete this paper.

Background
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Graphs {#Graphs}
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In this section, we formally introduce the graphs and the operations on graphs which we will 