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 , where denotes the number of perfect matchings in G, is the graph constructed from by deleting edges with an end vertex in {u,v}.
Extended Abstracts of the 6th Conference and Workshop on Mathematical Chemistry, Persian Gulf University, Bushehr, February 13 - 14, 2013 (Ed. M. Mogharrab)
Marandi, A., Nejah, A., & Behmaram, A. (2014). Perfect Matchings in Edge-Transitive Graphs. Iranian Journal of Mathematical Chemistry, 5(Supplement 1), 27-33. doi: 10.22052/ijmc.2014.7772
MLA
A. Marandi; A. H. Nejah; A. Behmaram. "Perfect Matchings in Edge-Transitive Graphs", Iranian Journal of Mathematical Chemistry, 5, Supplement 1, 2014, 27-33. doi: 10.22052/ijmc.2014.7772
HARVARD
Marandi, A., Nejah, A., Behmaram, A. (2014). 'Perfect Matchings in Edge-Transitive Graphs', Iranian Journal of Mathematical Chemistry, 5(Supplement 1), pp. 27-33. doi: 10.22052/ijmc.2014.7772
VANCOUVER
Marandi, A., Nejah, A., Behmaram, A. Perfect Matchings in Edge-Transitive Graphs. Iranian Journal of Mathematical Chemistry, 2014; 5(Supplement 1): 27-33. doi: 10.22052/ijmc.2014.7772
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