networks(deprecated)/fundcyc - Maple Help

networks

 fundcyc
 finds the cycle in a unicyclic undirected graph

 Calling Sequence fundcyc(eset, G)

Parameters

 G - graph or network e - set of edges of G

Description

 • Important: The networks package has been deprecated.  Use the superseding command GraphTheory[CycleBasis] instead.
 • Given a subset e of edges forming a unicyclic subgraph of a graph G, the edges forming the unique cycle are returned as a set.  It is assumed that only one cycle is present.
 • If no cycle exists then the empty set is returned.
 • When a spanning tree is known, fundcyc allows one to extract the fundamental cycles of a cycle basis by adding one edge at a time to the tree.
 • This routine is normally loaded via the command with(networks) but may also be referenced using the full name networks[fundcyc](...).

Examples

Important: The networks package has been deprecated.  Use the superseding command GraphTheory[CycleBasis] instead.

 > $\mathrm{with}\left(\mathrm{networks}\right):$
 > $G≔\mathrm{complete}\left(4\right):$
 > $\mathrm{sptree}≔\mathrm{edges}\left(\mathrm{spantree}\left(G\right)\right)$
 ${\mathrm{sptree}}{≔}\left\{{\mathrm{e1}}{,}{\mathrm{e3}}{,}{\mathrm{e6}}\right\}$ (1)
 > $e≔\mathrm{op}\left(1,\mathrm{edges}\left(G\right)∖\mathrm{sptree}\right)$
 ${e}{≔}{\mathrm{e2}}$ (2)
 > $\mathrm{fundcyc}\left(\mathrm{sptree}\phantom{\rule[-0.0ex]{0.5em}{0.0ex}}∪\phantom{\rule[-0.0ex]{0.5em}{0.0ex}}\left\{e\right\},G\right)$
 $\left\{{\mathrm{e2}}{,}{\mathrm{e3}}{,}{\mathrm{e6}}\right\}$ (3)