Construct a table that displays the number of directed paths of length 1 or 2 between each pair of vertices in the graph shown. **Understanding Directed Graph Paths****Constructing a Table for Directed Paths**To analyze the graph and determine the number of directed paths of length 1 or 2 between each pair of vertices, we can complete a table that represents these paths. Let's break down the process with a detailed explanation.### Graph DescriptionThe graph provided consists of 7 vertices labeled A, B, C, D, E, F, and G. Directed edges (arrows) indicate the direction from one vertex to another, outlining the possible paths.### Table DescriptionThe table is segmented into rows and columns representing the vertices. The rows indicate the starting vertices, while the columns represent the destination vertices. The table makes it easy to identify the number of directed paths of length 1 or 2 between pairs of vertices. Each cell in the table reflects the count of such paths.### Example Table| From \ To | A | B | C | D | E | F | G ||-----------|---|---|---|---|---|---|---|| A | 0 | 1 | 0 | 0 | 1 | 1 | 2 || B | 0 | 0 | 0 | 0 | 0 | 1 | 1 || C | 0 | 0 | 0 | 0 | 1 | 1 | 1 || D | 0 | 0 | 0 | 0 | 2 | 1 | 1 || E | 0 | 0 | 0 | 0 | 0 | 0 | 0 || F | 0 | 0 | 0 | 1 | 0 | 0 | 0 || G | 0 | 0 | 1 | 0 | 1 | 0 | 1 |### Explanation#### Path Analysis1. **From A to Other Vertices:** - A → B: 1 path of length 1. - A → E: 1 path of length 2 (via D). - A → F: 1 path of length 2 (via F). - A → G: 2 paths (one direct and one via C).2. **From B to Other Vertices:** - B → F: 1 path of length 1. - B

Fill table by the number of directed path between two vertices . If the number of directed path…

Construct a table that displays the number of directed paths of length 1 or 2 between each pair of vertices in the graph shown. A Complete the table below. To ABCD | E FG O| 10 0 1 1| 2 A в 1 co0 From D0 O0 E0 1 1 0| 2 1 1 D o|0| 0 |0 F 1

Construct a table that displays the number of directed paths of length 1 or 2 between each pair of vertices in the graph shown. A Complete the table below. To ABCD | E FG O| 10 0 1 1| 2 A в 1 co0 From D0 O0 E0 1 1 0| 2 1 1 D o|0| 0 |0 F 1

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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Question

Construct a table that displays the number of directed paths of length 1 or 2 between each pair of vertices in the graph shown.

**Understanding Directed Graph Paths**

**Constructing a Table for Directed Paths**

To analyze the graph and determine the number of directed paths of length 1 or 2 between each pair of vertices, we can complete a table that represents these paths. Let's break down the process with a detailed explanation.

### Graph Description

The graph provided consists of 7 vertices labeled A, B, C, D, E, F, and G. Directed edges (arrows) indicate the direction from one vertex to another, outlining the possible paths.

### Table Description

The table is segmented into rows and columns representing the vertices. The rows indicate the starting vertices, while the columns represent the destination vertices. The table makes it easy to identify the number of directed paths of length 1 or 2 between pairs of vertices. Each cell in the table reflects the count of such paths.

### Example Table

| From \ To | A | B | C | D | E | F | G |
|-----------|---|---|---|---|---|---|---|
| A | 0 | 1 | 0 | 0 | 1 | 1 | 2 |
| B | 0 | 0 | 0 | 0 | 0 | 1 | 1 |
| C | 0 | 0 | 0 | 0 | 1 | 1 | 1 |
| D | 0 | 0 | 0 | 0 | 2 | 1 | 1 |
| E | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
| F | 0 | 0 | 0 | 1 | 0 | 0 | 0 |
| G | 0 | 0 | 1 | 0 | 1 | 0 | 1 |

### Explanation

#### Path Analysis

1. **From A to Other Vertices:**
- A → B: 1 path of length 1.
- A → E: 1 path of length 2 (via D).
- A → F: 1 path of length 2 (via F).
- A → G: 2 paths (one direct and one via C).

2. **From B to Other Vertices:**
- B → F: 1 path of length 1.
- B

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