1. Discrete Mathematics

Try these first

1. 1.

   What defines a subgraph?

   Hint

   Think of a mini-version of a graph.

2. 2.

   Does a proper subgraph equal the original graph?

   Hint

   Remember, proper means smaller.

3. 3.

   What constitutes a proper subgraph?

   • A subgraph equal to G
   • A subgraph smaller than G
   • Any selected edges

   Hint

   Think of size comparisons.

4. 4.

   True or False: Every subgraph is also an induced subgraph?

   • True
   • False

   Hint

   Consider selective inclusion in induced subgraphs.

5. 5.

   Given two graphs, G and H with the same number of vertices but differing numbers of edges, prove they cannot be isomorphic.

   Hint

   Use the concept of edge mapping to illustrate this.

6. 6.

   Construct a graph with at least one cut vertex and one cut edge, providing a clear identification of each and demonstrating their impact on connectivity upon their removal.

   Hint

   Focus on the roles these points play together in your graph layout.