Graph Theory Questions Medium
In graph theory, a tree is a type of undirected graph that is acyclic (does not contain any cycles) and connected. It consists of a set of vertices (also known as nodes) and a set of edges that connect these vertices.
Specifically, a tree must satisfy the following properties:
1. It is connected, meaning that there is a path between any two vertices in the graph.
2. It is acyclic, meaning that there are no cycles or loops in the graph.
3. It is minimally connected, meaning that if any edge is removed from the graph, it will no longer be connected.
In a tree, there is a unique path between any pair of vertices, and the number of edges is exactly one less than the number of vertices. The vertex with no edges connected to it is called the root of the tree, and each other vertex is connected to the root by a unique path.
Trees are widely used in various applications, such as computer science, data structures, network design, and optimization problems. They provide a hierarchical structure and are used for organizing and representing data efficiently.