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An $Euler$ circuit of an undirected graph is a circuit in which each edge of the graph appears exactly once. Which of the following undirected graphs must have an $Euler$ circuit?

  1. A complete graph with $12$ vertices
  2. A complete graph with $13$ vertices
  3. A tree with $13$ vertices
  1. I and II
  2. III only
  3. II only
  4. I and III
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Euler circuit : Degree of every vertex should be EVEN.

I. A complete graph with 12 vertices. Degree of every vetrex will be 11.  
II. A complete graph with 13 vertices. Degree of every vetrex will be 12.  
III. A tree with 13 vertices. Degree of pendent nodes will be 1.
Answer:

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