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General trees are more difficult computationally,
and are enumerated by systematic augmentation, and then
removal of duplicates, the test of duplicity being
.
While general generation is computationally more difficult, it
is conceptually simple, and easy to define in terms of several
short algorithms.
![\begin{algorithm}
% latex2html id marker 140
[ht!]
\caption{$\mathit{Augmentati...
...ert $\mathit{Augment}(v,G)$\ into $S$
\ENDFOR
\end{algorithmic}\end{algorithm}](img61.png)
![\begin{algorithm}
% latex2html id marker 149
[ht!]
\caption{$\mathit{AugmentSet...
...cup \mathit{AugmentationsOfGraph}(g)$
\ENDFOR
\end{algorithmic}\end{algorithm}](img62.png)
With these two building blocks, it is now easy to generate all trees of
any given order.
![\begin{algorithm}
% latex2html id marker 158
[ht!]
\caption{$\mathit{Generate}(...
...tSetOfGraphs}(\mathit{Generate}(n-1))$
\ENDIF
\end{algorithmic}\end{algorithm}](img63.png)
Joshua Taylor
2005-04-27