networks[daughter]  find daughters in a directed tree

Calling Sequence


daughter(v, G)
daughter(G)


Parameters


G



graph or network

v



vertex or set of vertices





Description


•

Given a vertex, v, this routine reports the set of known daughters of v in the graph G. Such relationships are not always present in a given graph but are explicitly established by routines such as spantree() and shortpathtree(). Routines such as path() rely on this information when looking for paths and will return FAIL if it is not present.

•

If only the graph is mentioned then the actual daughter table indexed by vertices and specifying all known daughters in G is returned. Modifications to this table affect the actual graph.

•

In the two argument case, the first argument v may also be a set of vertices in which case the result is the set of daughters of the subgraph induced by v in G (ie. (the union of the daughters of each vertex in v minus the vertices in v).

•

The implementation of ancestor and daughter is completely separate from that of directed edges.

•

This routine is normally loaded using the command with(networks) but may also be referenced using the full name networks[daughter](...).



Examples


Important: The networks package has been deprecated. Use the superseding package GraphTheory instead.
>

$\mathrm{with}\left(\mathrm{networks}\right)\:$

>

$G:=\mathrm{petersen}\left(\right)\:$

>

$\mathrm{daughter}\left(1\,G\right)$

>

$T:=\mathrm{shortpathtree}\left(G\,1\right)\:$

>

$\mathrm{daughter}\left(8\,T\right)$

>

$\mathrm{daughter}\left(1\,T\right)$

$\left\{{2}{\,}{5}{\,}{6}\right\}$
 (3) 
>

$\mathrm{tbl}:=\mathrm{daughter}\left(T\right)$

${\mathrm{tbl}}{:=}{\mathrm{table}}\left(\left[{1}{\=}\left\{{2}{\,}{5}{\,}{6}\right\}{\,}{2}{\=}\left\{{3}{\,}{8}\right\}{\,}{3}{\=}\left\{{}\right\}{\,}{4}{\=}\left\{{}\right\}{\,}{5}{\=}\left\{{4}{\,}{9}\right\}{\,}{6}{\=}\left\{{7}{\,}{10}\right\}{\,}{7}{\=}\left\{{}\right\}{\,}{9}{\=}\left\{{}\right\}{\,}{8}{\=}\left\{{}\right\}{\,}{10}{\=}\left\{{}\right\}\right]\right)$
 (4) 
>

$\mathrm{path}\left(\left[9\,1\right]\,T\right)$



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