does this graph have a hamiltonian cycle? ### Graph Theory: Example of Undirected GraphThe diagram shown in the image represents an undirected graph consisting of eight nodes labeled from 'a' to 'h'. The graph illustrates various connections (edges) between these nodes. Understanding this type of graph is fundamental in the study of graph theory in computer science and mathematics.**Nodes:**- **a**- **b**- **c**- **d**- **e**- **f**- **g**- **h****Edges:**The connections between the nodes are represented by lines, showcasing the relationships or paths between them. Here, each edge is described with the two nodes it connects:- \(a \leftrightarrow b\)- \(a \leftrightarrow d\)- \(b \leftrightarrow c\)- \(b \leftrightarrow d\)- \(b \leftrightarrow e\)- \(c \leftrightarrow f\)- \(d \leftrightarrow e\)- \(e \leftrightarrow f\)- \(e \leftrightarrow g\)- \(e \leftrightarrow h\)- \(f \leftrightarrow h\)- \(g \leftrightarrow h\)### Key Concepts1. **Node or Vertex**: A single point in the graph (e.g., a, b, c).2. **Edge**: A line that connects two nodes (e.g., the edge connecting 'a' and 'b').### Applications- **Network Design**: Ensuring efficient and optimized routing paths.- **Social Networks**: Analyzing relationships and connections between individuals.- **Algorithms**: Basis for algorithms like Dijkstra's for shortest paths, and more.By studying this undirected graph, you can understand the underlying structure and relationships between these nodes, helping develop various algorithms and applications in computational theory and network analysis.

A Hamiltonian cycle is a path through a graph that visits each vertex exactly once and then returns…

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does this graph have a hamiltonian cycle?

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

Strongly Connected Components

A directed graph in which a path exists between all its pairs of vertices is called a strongly connected graph. A portion of the strongly connected directed graph that contains a path to reach from each vertex to other vertices is called a strongly connected component (SCC).

Question

does this graph have a hamiltonian cycle?

### Graph Theory: Example of Undirected Graph

The diagram shown in the image represents an undirected graph consisting of eight nodes labeled from 'a' to 'h'. The graph illustrates various connections (edges) between these nodes. Understanding this type of graph is fundamental in the study of graph theory in computer science and mathematics.

**Nodes:**

- **a**
- **b**
- **c**
- **d**
- **e**
- **f**
- **g**
- **h**

**Edges:**

The connections between the nodes are represented by lines, showcasing the relationships or paths between them. Here, each edge is described with the two nodes it connects:

- \(a \leftrightarrow b\)
- \(a \leftrightarrow d\)
- \(b \leftrightarrow c\)
- \(b \leftrightarrow d\)
- \(b \leftrightarrow e\)
- \(c \leftrightarrow f\)
- \(d \leftrightarrow e\)
- \(e \leftrightarrow f\)
- \(e \leftrightarrow g\)
- \(e \leftrightarrow h\)
- \(f \leftrightarrow h\)
- \(g \leftrightarrow h\)

### Key Concepts

1. **Node or Vertex**: A single point in the graph (e.g., a, b, c).
2. **Edge**: A line that connects two nodes (e.g., the edge connecting 'a' and 'b').

### Applications

- **Network Design**: Ensuring efficient and optimized routing paths.
- **Social Networks**: Analyzing relationships and connections between individuals.
- **Algorithms**: Basis for algorithms like Dijkstra's for shortest paths, and more.

By studying this undirected graph, you can understand the underlying structure and relationships between these nodes, helping develop various algorithms and applications in computational theory and network analysis.

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