4.5.1. Cartesian Product of Graphs

Try these first

1. 1.

   Define vertex connectivity in a graph.

   Hint

   Think of how many points need removal to break connection.

2. 2.

   What does the edge connectivity of a graph signify?

   Hint

   What breaks connections between nodes?

3. 3.

   What is the vertex connectivity used for?

   • To determine edge strength
   • To determine resilience against vertex removal
   • To count the number of edges

   Hint

   Think about how you would disconnect a graph.

4. 4.

   True or False: The Cartesian product of graphs only applies to simple graphs.

   • True
   • False

   Hint

   Recall the definitions of simple graphs.

5. 5.

   Given graphs G1 with vertex set {A, B} and edges {AB} and G2 with vertex set {1, 2} and edges {12}, describe the resulting Cartesian product and determine its connectivity characteristics.

   Hint

   Evaluate how edges define connections when their components share values.

6. 6.

   Suppose graph G1 has a vertex set of 4 vertices with a complete edge set and graph G2 has 3 disconnected vertices. Discuss the structural outcome of their Cartesian product.

   Hint

   Assess how each graph’s structure affects the new graph's edges.