et B
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
Related questions
Question
Determine an Euler circuit that begins with an vertex C in this Graph. 
Transcribed Image Text:### Educational Website Content: Graph Theory
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#### Introduction to Graph Theory:
Graph theory is a field within discrete mathematics that studies structures used to model pairwise relations between objects. These structures are called graphs, which consist of vertices (nodes) connected by edges.
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#### Example Graph:
Below is an example of a simple graph drawn on a lined sheet of paper. This graph consists of six vertices labeled \(A\), \(B\), \(C\), \(D\), \(E\), and \(F\), and several edges connecting them.
**Vertices**: The points labeled \(A\), \(B\), \(C\), \(D\), \(E\), and \(F\) are called vertices or nodes.
**Edges**: The lines connecting these vertices are called edges.
Let's describe the connections (edges) in this graph in more detail:
- The edge exists between vertices \(C\) and \(E\).
- The edge exists between vertices \(B\) and \(E\).
- The edge exists between vertices \(A\) and \(E\).
- The edge exists between vertices \(A\) and \(F\).
- The edge exists between vertices \(F\) and \(C\).
- The edge exists between vertices \(F\) and \(D\).
- The edge exists between vertices \(D\) and \(B\).
This particular graph forms a complex geometric shape, showing multiple connections between different vertices, which can be useful in studying various properties such as paths, cycles, and connectivity among nodes.
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#### Understanding Graph Notations:
Vertices are typically represented by dots or circles, while edges are represented by lines connecting these dots. Each edge can be labeled with weights or directions for more complex analysis, but this simple graph only shows undirected edges with equal weight.
By analyzing graphs, one can explore various domains such as computer networks, social networks, and biological networks. The sample graph above can serve as a starting point for understanding the basics of graph theory.
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