This is some functions for Pari/GP making calculations on labelled oriented trees (graph theory trees) as "vpar" vector of parent vertex numbers. Functions include

Vertices are numbered 1 to n. A tree is a vector vpar where vpar[v] is parent of v, or 0 if no parent. Such a representation is oriented in that there is a distinguished root (or roots for a forest) and labelled in that each vertex has a particular number. There are no other attributes etc.

The main use is to calculate or verify properties of specific trees of interest. Various functions like diameter are the same for any root or labelling so effectively act as on a "free" tree and the vertex numbers just for tree creation. Most functions are linear in the number of vertices so can be used on large trees.

The connections to Pari/GP specifics are at polynomials and Set()s for independent sets etc, matrices for some linear algebra or eigenvalues etc, permutations in relabelling, and then general compactness of GP for experimenting etc. is free software (free as in freedom), published under the terms of the GNU General Public License (v3 or higher). Download version 6 here, (415k, and sig), or compressed (107k)
vpar-6.tar.gz (479k, and sig)

Just is enough to run. The tar file includes some self-tests and some work-in-progress extras (most of which work but may change wildly). The sig files are Gnu PG ascii armoured signatures generated from my key.

See also gentreeg in the Nauty tools which generates free trees in this kind of vertex parent form (among other forms) and can be used command line or C.

This page Copyright 2017, 2018 Kevin Ryde, except for the GPLv3 logo which is Copyright Free Software Foundation and used here in accordance with its terms.

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