Which of the following is NOT a property of a tree in graph theory?A connected graph with n−1 edges where n is the number of vertices.There is exactly one path between any two vertices.A tree with n vertices has exactly n−1 edges.It may contain cycles.
Question
Which of the following is NOT a property of a tree in graph theory?A connected graph with n−1 edges where n is the number of vertices.There is exactly one path between any two vertices.A tree with n vertices has exactly n−1 edges.It may contain cycles.
Solution 1
The statement "It may contain cycles." is NOT a property of a tree in graph theory.
In graph theory, a tree is an undirected graph in which any two vertices are connected by exactly one path, and every non-empty graph that satisfies this condition is a tree. This means that no cycles (a path in which the first node is also the last node) can exist in a tree. Therefore, the presence of cycles contradicts the definition of a tree in graph theory.
Solution 2
The statement that is NOT a property of a tree in graph theory is "It may contain cycles." In graph theory, a tree is an undirected graph in which any two vertices are connected by exactly one path, and every edge connects two different vertices. Therefore, by definition, a tree cannot contain cycles.
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