The Pfaffian property of graphs on the Möbius strip based on topological resolution

Abstract

Recently, the problem about Pfaffian property of graphs has attracted much attention in the matching theory. Its significance stems from the fact that the number of perfect matchings in a graph G can be computed in polynomial time if G is Pfaffian. The Mobius strip with unique surface structure strip has potentially significant chirality properties in molecular chemistry. In this paper, we consider the Pfaffian property of graphs on the Mobius strip based on topological resolution. A sufficient condition for Pfaffian graphs on the Mobius strip is obtained. As its application, we characterize Pfaffian quadrilateral lattices on the Mobius strip.