  Let F = (V; A) be a digraph. Show that if u is k-edge-connected to v and v is k-edge-connected to w, then u is k-edge-connected to w.

Question

Let F = (V; A) be a digraph. Show that if u is k-edge-connected to v and v is k-edge-connected to w, then u is k-edge-connected to w.

Step 1

Connectivity:

To measure the connectedness of a digraph ‘F’, consider the minimum number of vertices and edges to be removed from the graph in to disconnect it.

Edge-connectivity:

It is the minimum number of edges whose removal results in a disconnected graph.

Vertex-connectivity:

It is the minimum number of vertices whose removal results in a disconnected graph.

Step 2

F = (V, A) is the given digraph.

If ‘u’ is k-edge connected to ‘v’, ‘v’ is k-edge connected to ‘w’ than ‘u’ is also k-edge connected to ‘w’ as it holds the transitive property.

According to the transitive property a relation ‘V’ on a set &lsq...

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Data Structures 