26.2. Graphs

Try these first

1. 1.

   What is a vertex in a graph?

   Hint

   Think of it as a point or location.

2. 2.

   What does an edge represent in a graph?

   Hint

   It's like a line connecting two points.

3. 3.

   Which of the following best describes a graph?

   • A linear data structure
   • A collection of vertices and edges
   • A static data type

   Hint

   Look for the option that describes the structure of a graph.

4. 4.

   True or False: A directed graph has edges that do not have a direction.

   • True
   • False

   Hint

   Think about how one-way streets function.

5. 5.

   Given a weighted undirected graph, use Dijkstra's algorithm to find the shortest path from vertex A to all other vertices, detailing each step.

   Hint

   Start by initializing distances and consider the order of vertex exploration.

6. 6.

   Using Prim’s algorithm, construct a minimum spanning tree for the following graph with weights on edges. Explain your steps.

   Hint

   Focus on finding the least expensive edge not yet included in the growing tree.