Which of the following statements about trees in graph theory is true?AA tree can contain cyclesBA tree is always a disconnected graphCA tree with n vertices has n−1 edgesDA tree has at least one cycle
Question
Which of the following statements about trees in graph theory is true?AA tree can contain cyclesBA tree is always a disconnected graphCA tree with n vertices has n−1 edgesDA tree has at least one cycle
Solution
The correct statement about trees in graph theory is "A tree with n vertices has n−1 edges".
Here's why:
A. A tree can contain cycles - This is false. By definition, a tree is a connected graph without cycles.
B. A tree is always a disconnected graph - This is false. A tree is always a connected graph, meaning there is a path from any vertex to any other vertex.
C. A tree with n vertices has n−1 edges - This is true. In a tree, every vertex (except the root) has exactly one parent, or one edge connecting it to the rest of the tree. So if there are n vertices, there are n-1 edges.
D. A tree has at least one cycle - This is false. As mentioned in point A, a tree does not contain cycles.
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