Questions: An Euler circuit travels all edges and ends back where it started.

Transcript text: An Euler circuit travels all edges and ends back where it started.

Solution

Solution Steps

Step 1: Understanding Euler Circuit

An Euler circuit is a path in a graph that visits every edge exactly once and returns to the starting vertex. For a graph to have an Euler circuit, it must be connected, and every vertex must have an even degree.

Step 2: Checking Graph Connectivity

Ensure that the graph is connected, meaning there is a path between any two vertices in the graph. This is a necessary condition for the existence of an Euler circuit.

Step 3: Verifying Vertex Degrees

Check the degree of each vertex in the graph. For an Euler circuit to exist, every vertex must have an even degree. If all vertices have even degrees, then an Euler circuit is possible.

Final Answer

An Euler circuit exists if the graph is connected and all vertices have even degrees.

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