# Achiral plane trees

Research output: Contribution to journalArticleResearchpeer-review

1 Citation (Scopus)

### Abstract

Harary and Robinson showed that the number an of achiral planted plane trees with n points coincides with the number pn of achiral plane trees with n points, for n ⩾ 2. They posed the problem of finding a natural structural correspondence which explains this coincidence. In the present paper this problem is answered by constructing two‐to‐one correspondences from certain sets of binary sequences to each of the sets of trees concerned, giving a structural basis for the equation 2an = 2pn. Answers are also supplied to similar correspondence‐type problems of Harary and Robinson, concerning planted plane trees, and achiral rooted plane trees. In addition, each of these four types of plane trees are counted with numbers of points and endpoints as the enumeration parameters. The results all show a symmetry with respect to the number of endpoints which is not shared by the set of all plane trees.

Original language English 189-208 20 Journal of Graph Theory 2 3 https://doi.org/10.1002/jgt.3190020303 Published - 1978 Yes

### Cite this

Wormald, Nicholas. / Achiral plane trees. In: Journal of Graph Theory. 1978 ; Vol. 2, No. 3. pp. 189-208.
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abstract = "Harary and Robinson showed that the number an of achiral planted plane trees with n points coincides with the number pn of achiral plane trees with n points, for n ⩾ 2. They posed the problem of finding a natural structural correspondence which explains this coincidence. In the present paper this problem is answered by constructing two‐to‐one correspondences from certain sets of binary sequences to each of the sets of trees concerned, giving a structural basis for the equation 2an = 2pn. Answers are also supplied to similar correspondence‐type problems of Harary and Robinson, concerning planted plane trees, and achiral rooted plane trees. In addition, each of these four types of plane trees are counted with numbers of points and endpoints as the enumeration parameters. The results all show a symmetry with respect to the number of endpoints which is not shared by the set of all plane trees.",
author = "Nicholas Wormald",
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In: Journal of Graph Theory, Vol. 2, No. 3, 1978, p. 189-208.

Research output: Contribution to journalArticleResearchpeer-review

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AU - Wormald, Nicholas

PY - 1978

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AB - Harary and Robinson showed that the number an of achiral planted plane trees with n points coincides with the number pn of achiral plane trees with n points, for n ⩾ 2. They posed the problem of finding a natural structural correspondence which explains this coincidence. In the present paper this problem is answered by constructing two‐to‐one correspondences from certain sets of binary sequences to each of the sets of trees concerned, giving a structural basis for the equation 2an = 2pn. Answers are also supplied to similar correspondence‐type problems of Harary and Robinson, concerning planted plane trees, and achiral rooted plane trees. In addition, each of these four types of plane trees are counted with numbers of points and endpoints as the enumeration parameters. The results all show a symmetry with respect to the number of endpoints which is not shared by the set of all plane trees.

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