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On the Enumeration of Tree-Rooted Maps

Published online by Cambridge University Press:  20 November 2018

R. C. Mullin
R. C. Mullin*
Affiliation:
University of Waterloo
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It is the purpose of this paper to show that many of the enumerative techniques available for counting rooted plane trees may be extended to tree-rooted maps, that is, rooted maps in which a spanning tree is distinguished as root tree. For example, tree-rooted maps are enumerated by partition, and the average number of trees in a rooted map with n edges is determined. An enumerative similarity between Hamiltonian rooted maps (that is, rooted maps with a distinguished Hamiltonian polygon) and tree-rooted maps is discussed. A 1-1 correspondence is established between treerooted maps with n edges and Hamiltonian rooted trivalent maps with 2n + 1 vertices in which the root vertex is exceptional, being divalent, both of which are in 1-1 correspondence with non-separable Hamiltonian-rooted triangularized digons with n internal vertices, where both the latter are as defined in (2).

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 19 , 1967 , pp. 174 - 183
Copyright
Copyright © Canadian Mathematical Society 1967

References

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