Graphene has been found to be an attractive material since its discovery in 2004 and has drawn enormous interest among researchers owing to its intrinsic electronic and magnetic properties. An indefinitely large graphene sheet, if cut along the two edge directions, can generate two distinct, well-defined small graphene nanoribbons (GNRs), which may be classified into “zigzag” edge (1, transpoly...

We define the anti-forcing number of a perfect matching M of a graph G as the minimal number of edges of Gwhose deletion results in a subgraph with a unique perfect matching M , denoted by af (G,M). The anti-forcing number of a graph proposed by Vukičević and Trinajstić in Kekulé structures of molecular graphs is in fact the minimum anti-forcing number of perfect matchings. For plane bipartite ...