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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does this graph have a hamiltonian cycle?

Transcribed Image Text:### 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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