**Graph Isomorphism Selection****Task:** Select the function \( f \) that is an isomorphism from graph \( G \) to graph \( G' \).**Graphs Description:**- **Graph \( G \):** - Consists of 5 vertices labeled \( a, b, c, d, \) and \( e \). - Edges are present between the following pairs: \( (a, b), (a, d), (b, c), (b, e), (c, d) \).- **Graph \( G' \):** - Consists of 5 vertices labeled \( 1, 2, 3, 4, \) and \( 5 \). - Edges are present between the following pairs: \( (3, 1), (3, 5), (1, 4), (1, 5), (5, 2) \).**Options for Isomorphism \( f \):**- Option 1: \( f(a) = 3, f(b) = 5, f(c) = 4, f(d) = 2, f(e) = 1 \)- Option 2: \( f(a) = 3, f(b) = 5, f(c) = 2, f(d) = 4, f(e) = 3 \)- Option 3: \( f(a) = 3, f(b) = 4, f(c) = 2, f(d) = 5, f(e) = 1 \)- Option 4: \( f(a) = 3, f(b) = 5, f(c) = 2, f(d) = 4, f(e) = 1 \)**Goal:** Determine which function \( f \) correctly maps vertices of graph \( G \) to graph \( G' \) while preserving the adjacency between vertices.

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Select the function f that is an isomorphism from G to G b 3 5 2 G' G f(a) = 3, f(b) = 5, f(c) = 4, f(d) = 2, f(e) = 1 f(a) = 3, f(b) = 5, f(c) = 2, f(d) = 4, f(e) = 3 f(a) = 3, f(b) = 4, f(c) = 2, f(d) = 5, f(e) = 1 ) f(a) = 3, f(b) = 5, f(c) = 2, f(d) = 4, f(e) = 1

Select the function f that is an isomorphism from G to G b 3 5 2 G' G f(a) = 3, f(b) = 5, f(c) = 4, f(d) = 2, f(e) = 1 f(a) = 3, f(b) = 5, f(c) = 2, f(d) = 4, f(e) = 3 f(a) = 3, f(b) = 4, f(c) = 2, f(d) = 5, f(e) = 1 ) f(a) = 3, f(b) = 5, f(c) = 2, f(d) = 4, f(e) = 1

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

Problem 1PE

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Concept explainers

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Object Oriented Programming System (OOPs) is a programming model built on the perception of “objects” that contains data and methods. The major purpose of Object Oriented Programming is to increase the maintainability and flexibility of programs. Object Oriented Programming gets together data and its behavior (methods) in a single location (object) which makes it easier to understand.

Question

**Graph Isomorphism Selection**

**Task:** Select the function \( f \) that is an isomorphism from graph \( G \) to graph \( G' \).

**Graphs Description:**

- **Graph \( G \):**
- Consists of 5 vertices labeled \( a, b, c, d, \) and \( e \).
- Edges are present between the following pairs: \( (a, b), (a, d), (b, c), (b, e), (c, d) \).

- **Graph \( G' \):**
- Consists of 5 vertices labeled \( 1, 2, 3, 4, \) and \( 5 \).
- Edges are present between the following pairs: \( (3, 1), (3, 5), (1, 4), (1, 5), (5, 2) \).

**Options for Isomorphism \( f \):**

- Option 1: \( f(a) = 3, f(b) = 5, f(c) = 4, f(d) = 2, f(e) = 1 \)
- Option 2: \( f(a) = 3, f(b) = 5, f(c) = 2, f(d) = 4, f(e) = 3 \)
- Option 3: \( f(a) = 3, f(b) = 4, f(c) = 2, f(d) = 5, f(e) = 1 \)
- Option 4: \( f(a) = 3, f(b) = 5, f(c) = 2, f(d) = 4, f(e) = 1 \)

**Goal:** Determine which function \( f \) correctly maps vertices of graph \( G \) to graph \( G' \) while preserving the adjacency between vertices.

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