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1. Define a path between two vertices. 2. What is a simple path? 3. What is a cy

ID: 3773382 • Letter: 1

Question

1. Define a path between two vertices.

2. What is a simple path?

3. What is a cycle?

4. What is a simple cycle?

5. What is a complete graph?

6. What is a self edge?

7. What is a weighted graph?

8. What are two differences between a directed graph and an undirected graph?

9. What are the two most common implementations of a graph?

10. How does the depth-first search (DFS) strategy of graph traversal differ from the breadth-first search (BFS) strategy?

11. What is a spanning tree?

12. What is a minimum spanning tree?

13. How is the cost of a spanning tree calculated?

14. What is the shortest path between two vertices in a weighted graph?

15. What is a planar graph?

Explanation / Answer

1. The path between two vertices of a graph is defined as length of shortest path between the two vertices, if there exists one, and otherwise the distance becomes infinity.

2. A simple path is a path in which there are no repeating vertices.

3. A cycle in a graph G, also known as a circuit if the start vertex is not given, can be defined as a subset of set of edges in G which forms a path in such a way that the start node of the path corresponds to the end node.

4. A simple cycle can be defined as a closed walk in which vertices and edges are not repeated apart from start and end vertex.

5. A complete graph is defined as simple undirected graph where a unique edge connect a pair of unique vertices. is connected by a unique edge