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• W1488229411 abstract "We define the anti-forcing number of a perfect matching M of a graph G as the minimal number of edges of G whose 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 graph G with a perfect matching M, we obtain a minimax result: af(G,M) equals the maximal number of M-alternating cycles of G where any two either are disjoint or intersect only at edges in M. For a hexagonal system H, we show that the maximum anti-forcing number of H equals the Fries number of H. As a consequence, we have that the Fries number of H is between the Clar number of H and twice. Further, some extremal graphs are discussed." @default.
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• W1488229411 date "2016-03-01" @default.
• W1488229411 modified "2023-10-14" @default.
• W1488229411 title "Anti-forcing numbers of perfect matchings of graphs" @default.
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• W1488229411 doi "https://doi.org/10.1016/j.dam.2015.08.024" @default.
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