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GO Classes 2024 | IIITH Mock Test 5 | Question: 49

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Which of the following is/are correct?

  • $S_1:$ A connected graph of at least $2$ vertices has an Euler circuit if and only if degree of every vertex is even.
  • $S_2:$ A connected graph has an Euler path but not an Euler circuit if and only if there are at most two vertices with odd degree.
  1. $S_1$ only
  2. $S_2$ only
  3. Both $S_1$ and $S_2$
  4. Neither $S_1$ nor $S_2$
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$S_2$ is actually not TRUE as it is “iff” and not “if”.

A connected graph has an Euler path but not Euler circuit if and only if there are exactly two vertices of odd degree.

So, the correct answer is $(A)$.
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