28.1.4. Edge Cut

Try these first

1. 1.

   Define an edge cut in your own words.

   Hint

   Think about how removing connections can affect overall connectivity.

2. 2.

   What is edge connectivity?

   Hint

   Consider how many connections are crucial for keeping a graph intact.

3. 3.

   What defines an edge cut in a graph?

   • A set of vertices
   • A subset of edges that keeps the graph connected
   • A group of edges whose removal disconnects the graph

   Hint

   Focus on the outcomes of edge removal related to connectivity.

4. 4.

   True or False: Every connected graph has at least one edge cut.

   • True
   • False

   Hint

   Consider the nature of connectivity in graphs.

5. 5.

   Consider a graph with vertices labeled A, B, C, D, and edges (A, B), (B, C), (C, D), (D, A), (B, D). Identify and list all edge cuts, and calculate the edge connectivity.

   Hint

   Analyze how each edge interacts with the others connected.

6. 6.

   Given a graph example where edge connectivity = 1, construct such a graph and justify your answer by identifying its edge cut.

   Hint

   Visualize scenarios where minimal edge connection is pertinent.