1. The problem is to understand the properties of a tree in graph theory. 2. A tree is defined as a connected graph with no circuits (cycles). 3. Important properties of a tree include: - It has no circuits. - It is connected. - It has exactly $n-1$ edges if there are $n$ vertices. 4. The options given are: - odd vertex - circuit - even vertex - pendant vertex 5. Since a tree has no circuits, the correct property that a tree does not have is a "circuit". 6. Pendant vertices (vertices with degree 1) are common in trees. 7. Therefore, the answer is that a tree is a connected graph without any circuit.