On the enumeration of certain graceful graphs
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:
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© Springer-Verlag 1978