On the enumeration of certain graceful graphs

  • C. C. Chen
Contributed Papers
Part of the Lecture Notes in Mathematics book series (LNM, volume 686)


A graceful graph on n vertices is said to be simple if each of its connected components has at most one cycle and the component containing the edge with end points labelled 1 and n has no cycle. Let sn and tn denote the numbers of simple graceful graphs and graceful trees on n vertices respectively. Then tn≦sn≦p(An-2) where p(An-2) is the permanent (plus determinant) of the (n-2)×(n-2) matrix An-2=(aij) defined by: More specifically, let ci denote the number of simple graceful graphs on n vertices with i cycles (i=0,1,2,...,k, where k=[(n-2)/3]). Then we have


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  1. (1).
    I. Cahit, "Are all complete binary trees graceful?" Amer. Math. Monthly 83(1976), 35–37.MathSciNetCrossRefMATHGoogle Scholar

Copyright information

© Springer-Verlag 1978

Authors and Affiliations

  • C. C. Chen
    • 1
  1. 1.Department of MathematicsNanyang UniversitySingapore

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