Trees special type graph from "summary" of Introduction to Graph Theory by Douglas Brent West
A tree is a special type of graph that is simple in structure yet rich in properties. A tree is an undirected graph that is connected and has no cycles. This means that a tree consists of a set of vertices connected by edges, with the property that there is a unique path between any two vertices in the tree. The simplicity of trees makes them a fundamental object of study in graph theory. Trees provide a natural way to model hierarchical relationships, such as family trees or organizational structures. In addition, trees have important applications in computer science, where they are used to represent data structures such as binary trees or search trees. One key property of trees is that they have a unique path between any two vertices. This property is known as the tree property, and it is what distinguishes trees from other types of graphs. Another important property of trees is that they are minimally connected, meaning that removing any edge from a tree will disconnect the graph. Trees can also be characterized by their size, which is the number of vertices in the tree. The most basic type of tree is the path, which consists of a single line of vertices connected by edges. Other types of trees include stars, which consist of a central vertex connected to all other vertices, and binary trees, which consist of nodes with at most two children.- Trees are a simple yet powerful concept in graph theory that have wide-ranging applications in various fields. By studying the properties of trees, researchers can gain insights into the structure and behavior of complex systems, making trees a versatile and valuable tool in the study of graphs.
