Multiple choice general knowledge science & technology

A graph G has an Euler cycle, then G is connected and every vertex has:

  1. even degree

  2. odd degree

  3. at least one loop

  4. none of these
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A Correct answer
Explanation

Euler's theorem states that a connected graph has an Euler cycle (closed trail using every edge exactly once) if and only if every vertex has even degree. This is because each time an Euler trail enters a vertex, it must also exit, requiring paired edges. Loops contribute 2 to the degree count.

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