, Volume 9, Issue 1, pp 85–89 | Cite as

Solution to a problem of C. D. Godsil regarding bipartite graphs with unique perfect matching

  • R. Simion
  • D. -S. Cao


We give the solution to the following question of C. D. Godsil[2]: Among the bipartite graphsG with a unique perfect matching and such that a bipartite graph obtains when the edges of the matching are contracted, characterize those having the property thatG+G, whereG+ is the bipartite multigraph whose adjacency matrix,B+, is diagonally similar to the inverse of the adjacency matrix ofG put in lower-triangular form. The characterization is thatG must be obtainable from a bipartite graph by adding, to each vertex, a neighbor of degree one. Our approach relies on the association of a directed graph to each pair (G, M) of a bipartite graphG and a perfect matchingM ofG.

AMS subject classification (1980)

05 C 05 06 A10 


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Copyright information

© Akadémiai Kiadó 1989

Authors and Affiliations

  • R. Simion
    • 1
  • D. -S. Cao
    • 2
  1. 1.Department of MathematicsGeorge Washington UniversityWashington, D.C.USA
  2. 2.Mathematics DepartementHua Zhong University of Science and Technology WuhanHubei ProvincePeople's Republic of China

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