Abstract
We find recursive formulae for the number of perfect matchings in a graph G by splitting G into subgraphs H and Q. We use these formulas to count perfect matching of P hypercube Qn. We also apply our formulas to prove that the number of perfect matching in an edge-transitive graph is (ܩ ) = (2ݍ / ) (ܩ \{ݑ ,ݒ }), where (ܩ ) denotes the number of perfect matchings in G, ܩ \{ݑ ,ݒ } is the graph constructed from ܩ by deleting edges with an end vertex in {u,v} and uv E(G).
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