Möbius inversion on a poset of a graph and its acyclic subgraphs Original Research Article

Several chemical models for resonance energy of conjugated hydrocarbons are formulated in terms of a graph and its acyclic subgraphs. The resonance energy in these models is expressed by a truncated cluster expansion in terms of acyclic subgraphs. In order to efficiently perform the complete expansion, one needs to know the Möbius function for the pertinent partially ordered set. In the present paper a formula for the Möbius function in the poset is derived and discussed.