24.1. Graph Theory Basics

Try these first

1. 1.

   What does a graph consist of?

   Hint

   Think of it as connections between points.

2. 2.

   In a simple graph, can you have multiple edges between two vertices?

   Hint

   Recall the definition of a simple graph.

3. 3.

   What defines a simple graph?

   • A graph with self-loops
   • A graph with at most one edge between two vertices
   • A graph needing multiple edges

   Hint

   Think about the basic properties of simple graphs.

4. 4.

   True or False: In a directed graph, the order of vertices in edges matters.

   • True
   • False

   Hint

   Consider the nature of direction in edges.

5. 5.

   Given a graph with 6 vertices, each having a degree of 3, use the handshaking theorem to find the number of edges.

   Hint

   Apply the relationship between vertices' degrees and edges carefully.

6. 6.

   Construct a bipartite graph with 4 vertices in one set and 3 vertices in another. Describe its properties.

   Hint

   Visualize your graph to understand the connections.