What is the number of connected components for each of the following graphs? **Transcription for Educational Website****Title: Understanding Connected Components in Graphs**---**Question:**What is the number of connected components for each of the following graphs?---**Graph (a):**- **Description:** - This graph consists of two distinct parts: 1. A diamond-shaped subgraph with vertices labeled $ a, b, c, d $. 2. A linear segment with vertices labeled $ f, g, h $. - Additionally, vertex $ e $ is isolated. - **Answer:** - The correct number of connected components is 3 (not 7 as shown in the incorrect answer).---**Graph (b):**- **Description:** - A star-shaped configuration with intersecting lines forming a hexagon. - Vertices are labeled $ u, v, w, x, y, z $ in a connected hexagon.- **Answer:** - The correct number of connected components is 1 (not 6 as shown in the incorrect answer).---**Graph (c):**- **Description:** - This graph includes: 1. A central node $ i $ connected to nodes $ a, b, c, d, e, h, j $. 2. A self-loop at node $ c $. 3. A separate linear segment with vertices $ f, g $.- **Answer:** - The correct number of connected components is 2 (not 8 as shown in the incorrect answer). ---**Note:** In graph theory, a connected component is a maximal set of vertices such that each pair of vertices is connected by a path. Understanding the number of connected components helps in analyzing the structure and connectivity of graphs.

A connected component of an undirected graph is a maximal set of nodes such that each pair of nodes…

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What is the number of connected components for each of the following graphs? (a) b a d

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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What is the number of connected components for each of the following graphs?

**Transcription for Educational Website**

**Title: Understanding Connected Components in Graphs**

---

**Question:**
What is the number of connected components for each of the following graphs?

---

**Graph (a):**

- **Description:**
- This graph consists of two distinct parts:
1. A diamond-shaped subgraph with vertices labeled $ a, b, c, d $.
2. A linear segment with vertices labeled $ f, g, h $.
- Additionally, vertex $ e $ is isolated.

- **Answer:**

- The correct number of connected components is 3 (not 7 as shown in the incorrect answer).

---

**Graph (b):**

- **Description:**
- A star-shaped configuration with intersecting lines forming a hexagon.
- Vertices are labeled $ u, v, w, x, y, z $ in a connected hexagon.

- **Answer:**

- The correct number of connected components is 1 (not 6 as shown in the incorrect answer).

---

**Graph (c):**

- **Description:**
- This graph includes:
1. A central node $ i $ connected to nodes $ a, b, c, d, e, h, j $.
2. A self-loop at node $ c $.
3. A separate linear segment with vertices $ f, g $.

- **Answer:**

- The correct number of connected components is 2 (not 8 as shown in the incorrect answer).

---

**Note:** In graph theory, a connected component is a maximal set of vertices such that each pair of vertices is connected by a path. Understanding the number of connected components helps in analyzing the structure and connectivity of graphs.

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