Determine if the graph contains an Euler circuit. If so, identify an Euler circuit on the graph by number- ing the sequence of edges in the order traveled. If not, explain.
Determine if the graph contains an Euler circuit. If so, identify an Euler circuit on the graph by number- ing the sequence of edges in the order traveled. If not, explain.
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
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Transcribed Image Text:**Question 6:** Determine if the graph contains an Euler circuit. If so, identify an Euler circuit on the graph by numbering the sequence of edges in the order traveled. If not, explain.
**Graph Description:**
The graph is composed of two triangles connected by a series of interconnected vertices, forming a bridge-like structure. There are a total of 8 vertices:
- The two triangles are joined at one of their bases, creating a rectangular shape.
- Each vertex within the inner region connects to three vertices, making the graph symmetrical along the vertical axis.
**Explanation:**
To determine if an Euler circuit exists, check the degree of each vertex. An Euler circuit requires that all vertices in the graph have even degrees.
**Vertex Degrees:**
- Top left and top right vertices: Degree 3
- Bottom left and bottom right vertices: Degree 3
- Top center and bottom center vertices: Degree 2
- Middle vertex: Degree 4
Since not all vertices have an even degree, the graph does not contain an Euler circuit.
Expert Solution
Step 1
A circuit is a path that starts and ends at the same vertex. A Euler circuit is a circuit that passes through all the edges in a graph so that no edge is repeated. If all the vertices of a graph have even degree, then the graph will contain a Euler circuit.
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