IsTwoEdgeConnected - Maple Help
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GraphTheory

 IsTwoEdgeConnected
 test if graph is two-edge connected
 TwoEdgeConnectedComponents
 compute two-edge connected components of graph

 Calling Sequence IsTwoEdgeConnected(G) TwoEdgeConnectedComponents(G)

Parameters

 G - graph

Description

 • A connected graph G is 2-edge connected if removal of any edge from G does not disconnect G.  The IsTwoEdgeConnected command returns true if G is 2-edge connected and false otherwise.
 • TwoEdgeConnectedComponents returns the 2-edge connected components of a graph G.  The output is a list of lists of vertices of G, each being the list of vertices of a component.

Examples

 > $\mathrm{with}\left(\mathrm{GraphTheory}\right):$
 > $\mathrm{IsTwoEdgeConnected}\left(\mathrm{CycleGraph}\left(4\right)\right)$
 ${\mathrm{true}}$ (1)
 > $\mathrm{IsTwoEdgeConnected}\left(\mathrm{PathGraph}\left(4\right)\right)$
 ${\mathrm{false}}$ (2)
 > $G≔\mathrm{Graph}\left(\left\{\left\{a,b\right\},\left\{a,c\right\},\left\{a,h\right\},\left\{a,i\right\},\left\{b,c\right\},\left\{c,d\right\},\left\{d,e\right\},\left\{d,f\right\},\left\{e,f\right\},\left\{h,i\right\}\right\}\right):$
 > $\mathrm{IsTwoEdgeConnected}\left(G\right)$
 ${\mathrm{false}}$ (3)
 > $\mathrm{DrawGraph}\left(G\right)$
 > $\mathrm{TwoEdgeConnectedComponents}\left(G\right)$
 $\left[\left[{d}{,}{e}{,}{f}\right]{,}\left[{a}{,}{b}{,}{c}{,}{h}{,}{i}\right]\right]$ (4)