EdgeConnectivity - Maple Help

GraphTheory

 EdgeConnectivity
 compute edge connectivity of a graph
 VertexConnectivity
 compute vertex connectivity of a graph

 Calling Sequence EdgeConnectivity(G) VertexConnectivity(G)

Parameters

 G - graph

Description

 • EdgeConnectivity returns the edge connectivity of a graph, that is the minimum number of edges whose removal disconnects the graph. A set of such edges is called an edge-cut.  You can use the IsCutSet command to test whether a set of edges is an edge-cut.
 • VertexConnectivity returns the vertex connectivity of a graph, that is the minimum number of vertices whose removal disconnects the graph.
 • By an elementary theorem of graph theory, the vertex connectivity of a graph is less than or equal to the edge connectivity, which is less than or equal to the minimum degree.

Examples

 > $\mathrm{with}\left(\mathrm{GraphTheory}\right):$
 > $G≔\mathrm{Graph}\left(\left\{\left\{1,2\right\},\left\{1,3\right\},\left\{1,4\right\},\left\{2,3\right\},\left\{3,4\right\},\left\{4,5\right\},\left\{4,6\right\},\left\{5,6\right\}\right\}\right)$
 ${G}{≔}{\mathrm{Graph 1: an undirected unweighted graph with 6 vertices and 8 edge\left(s\right)}}$ (1)
 > $\mathrm{DrawGraph}\left(G\right)$
 > $\mathrm{EdgeConnectivity}\left(G\right)$
 ${2}$ (2)
 > $\mathrm{VertexConnectivity}\left(G\right)$
 ${1}$ (3)
 > $\mathrm{MinimumDegree}\left(G\right)$
 ${2}$ (4)
 > $\mathrm{with}\left(\mathrm{SpecialGraphs}\right):$
 > $P≔\mathrm{PetersenGraph}\left(\right)$
 ${P}{≔}{\mathrm{Graph 2: an undirected unweighted graph with 10 vertices and 15 edge\left(s\right)}}$ (5)
 > $\mathrm{VertexConnectivity}\left(P\right)$
 ${3}$ (6)
 > $\mathrm{EdgeConnectivity}\left(P\right)$
 ${3}$ (7)
 > $\mathrm{MinimumDegree}\left(P\right)$
 ${3}$ (8)