Algorithms Analysis 2025 – 400 Free Practice Questions to Pass the Exam

Question: 1 / 400

True/False: A tree is a type of graph that contains cycles.

True

False

A tree is indeed a type of graph, and by definition, it is a connected acyclic graph. This means that a tree does not contain any cycles. Every two vertices in a tree are connected by exactly one simple path, ensuring that no loops or cycles exist within the structure. Additionally, trees have a hierarchical structure with a single root node, and they are characterized by having \(n\) vertices and \(n-1\) edges, where \(n\) represents the number of nodes in the tree.

In contrast, the presence of cycles would contradict the basic properties of a tree, making the assertion that a tree contains cycles false. This fundamental characteristic distinguishes trees from other types of graphs, such as directed or undirected graphs, which may contain cycles. Understanding this distinction is essential in graph theory and algorithms that utilize tree structures.

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