**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.

We have to find given network is Euler circuit or not.

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

Holt Mcdougal Larson Pre-algebra: Student Edition 2012

1st Edition

ISBN:9780547587776

Author:HOLT MCDOUGAL

Publisher:HOLT MCDOUGAL

Chapter12: Angle Relationships And Transformations

Section12.5: Reflections And Symmetry

Problem 20E

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Question

**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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