The Merrifield–Simmons Conjecture Holds for Bipartite Graphs


  • Contract grant sponsor: European Social Fund (ESF) of the European Union (EU).


Let math formula be a graph and math formula the number of independent (vertex) sets of G. Then the Merrifield–Simmons conjecture states that the sign of the term math formula only depends on the parity of the distance of the vertices math formula in G. We prove that the conjecture holds for bipartite graphs by considering a generalization of the term, where vertex subsets instead of vertices are deleted.