(2) 1. Is the following graph strongly connected? If not, is it weakly connected? If not, how many connected components does it have? b (2) 2. Is the following graph strongly connected? If not, is it weakly connected? If not, how many connected components does it have? 11 f 10 12 1 8 7 6 5

Database System Concepts
7th Edition
ISBN:9780078022159
Author:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan
Publisher:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan
Chapter1: Introduction
Section: Chapter Questions
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**Graph Connectivity Analysis**

**Question 1:**

1. Is the following graph strongly connected? _______

   If not, is it weakly connected? _______

   If not, how many connected components does it have? _______

**Graph Description:**

- This graph contains six vertices labeled a, b, c, d, e, and f.
- Connections:
  - a → d
  - b → a, b → c
  - c → b, c → e
  - e → f
  - f → c

**Question 2:**

2. Is the following graph strongly connected? _______

   If not, is it weakly connected? _______

   If not, how many connected components does it have? _______

**Graph Description:**

- This graph contains twelve vertices labeled from 1 to 12.
- Connections between vertices form a directed circle with additional connections across the circle, possibly indicating a more complex structure.

**Instructions for Analysis:**

- A graph is **strongly connected** if there is a path between any pair of vertices in both directions.
- A graph is **weakly connected** if replacing all directed edges with undirected makes the graph connected.
- Count the number of **connected components** if the graph is not weakly connected. A connected component is a subgraph where any two vertices are connected by a path, and no vertex in the component is connected to any vertex not in the component.
Transcribed Image Text:**Graph Connectivity Analysis** **Question 1:** 1. Is the following graph strongly connected? _______ If not, is it weakly connected? _______ If not, how many connected components does it have? _______ **Graph Description:** - This graph contains six vertices labeled a, b, c, d, e, and f. - Connections: - a → d - b → a, b → c - c → b, c → e - e → f - f → c **Question 2:** 2. Is the following graph strongly connected? _______ If not, is it weakly connected? _______ If not, how many connected components does it have? _______ **Graph Description:** - This graph contains twelve vertices labeled from 1 to 12. - Connections between vertices form a directed circle with additional connections across the circle, possibly indicating a more complex structure. **Instructions for Analysis:** - A graph is **strongly connected** if there is a path between any pair of vertices in both directions. - A graph is **weakly connected** if replacing all directed edges with undirected makes the graph connected. - Count the number of **connected components** if the graph is not weakly connected. A connected component is a subgraph where any two vertices are connected by a path, and no vertex in the component is connected to any vertex not in the component.
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