Contrast the Hamilton path and cycle with the Euler path and cycle.<<<image here>>> The image depicts a graph consisting of six nodes, labeled with the numbers 1 through 6. The nodes are interconnected with edges, forming a network. Here is a detailed explanation:- Node 1 is connected to Node 2 and Node 5.- Node 2 is connected to Node 1, Node 3, and Node 5.- Node 3 is connected to Node 2 and Node 4.- Node 4 is connected to Node 3, Node 5, and Node 6.- Node 5 is connected to Node 1, Node 2, and Node 4.- Node 6 is connected to Node 4.This graph can be described as an undirected graph where each connection or edge is a line that indicates a mutual link between nodes. The graph can be useful for illustrating relationships or paths in network theory, computer science, or related educational fields.

Answered: 6 4 3 5 2 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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Contrast the Hamilton path and cycle with the Euler path and cycle.

<<<image here>>>

The image depicts a graph consisting of six nodes, labeled with the numbers 1 through 6. The nodes are interconnected with edges, forming a network. Here is a detailed explanation:

- Node 1 is connected to Node 2 and Node 5.
- Node 2 is connected to Node 1, Node 3, and Node 5.
- Node 3 is connected to Node 2 and Node 4.
- Node 4 is connected to Node 3, Node 5, and Node 6.
- Node 5 is connected to Node 1, Node 2, and Node 4.
- Node 6 is connected to Node 4.

This graph can be described as an undirected graph where each connection or edge is a line that indicates a mutual link between nodes. The graph can be useful for illustrating relationships or paths in network theory, computer science, or related educational fields.

Expert Solution

Step 1

Solution:

The set of ordered pairs = { ( 1,2), ( 1,5) , ( 2,1), ( 2,3), ( 2,5), (3,2), (3,4), ( 4,3), ( 4,5), ( 4,6) , ( 5,1), ( 5,2), ( 5,4), ( 6, 4) }

a. Hamilton path: It is a graph that only visits each vertex once.

1-2-3-4-5

b. Hamilton cycle: A Hamiltonian cycle is a Hamiltonian Path with an edge (in the graph) connecting the Hamiltonian Path's last and first vertices.

1-2-3-4-5-1

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