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The Merrifield–Simmons Conjecture Holds for Bipartite Graphs

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

Abstract

Let inline image be a graph and inline image the number of independent (vertex) sets of G. Then the Merrifield–Simmons conjecture states that the sign of the term inline image only depends on the parity of the distance of the vertices inline image 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.

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