Is the network an Euler circuit? Can this network can be traversed? F A E B D C

Algebra and Trigonometry (6th Edition)
6th Edition
ISBN:9780134463216
Author:Robert F. Blitzer
Publisher:Robert F. Blitzer
ChapterP: Prerequisites: Fundamental Concepts Of Algebra
Section: Chapter Questions
Problem 1MCCP: In Exercises 1-25, simplify the given expression or perform the indicated operation (and simplify,...
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**Is the network an Euler circuit? Can this network be traversed?**

In the image, there is a geometrical figure represented as a hexagon with vertices labeled A, B, C, D, E, and F. Each vertex is connected to its adjacent vertices by edges, forming a closed loop. These vertices and edges create a hexagonal shape, suggesting that it may be an Euler circuit.

**Explanation:**

An Euler circuit in a graph is a circuit that uses every edge of the graph exactly once and starts and ends at the same vertex. For a connected graph to have an Euler circuit, each vertex must have an even degree (an even number of edges).

Each vertex of the hexagon is connected to two other vertices (i.e., it has a degree of 2). Since all vertices have an even degree and the hexagon is a connected graph, the given network is, indeed, an Euler circuit, which means this network can be traversed by starting and ending at the same vertex and using each edge exactly once.
Transcribed Image Text:**Is the network an Euler circuit? Can this network be traversed?** In the image, there is a geometrical figure represented as a hexagon with vertices labeled A, B, C, D, E, and F. Each vertex is connected to its adjacent vertices by edges, forming a closed loop. These vertices and edges create a hexagonal shape, suggesting that it may be an Euler circuit. **Explanation:** An Euler circuit in a graph is a circuit that uses every edge of the graph exactly once and starts and ends at the same vertex. For a connected graph to have an Euler circuit, each vertex must have an even degree (an even number of edges). Each vertex of the hexagon is connected to two other vertices (i.e., it has a degree of 2). Since all vertices have an even degree and the hexagon is a connected graph, the given network is, indeed, an Euler circuit, which means this network can be traversed by starting and ending at the same vertex and using each edge exactly once.
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