eingängigkeit

Eingängigkeit is a concept in graph theory, a branch of mathematics that studies the properties of graphs, which are structures consisting of vertices (or nodes) connected by edges (or links). A graph is considered eingängig if it has exactly one vertex with a degree of one, meaning that this vertex is connected to only one other vertex. This unique vertex is often referred to as a "leaf" or "pendant vertex."

The concept of eingängigkeit is particularly relevant in the study of trees, which are a type of graph that is connected and acyclic (contains no cycles). In a tree, every vertex except the root has exactly one edge connecting it to the rest of the tree, making it a leaf. Therefore, a tree with exactly one leaf is considered eingängig.

The property of eingängigkeit is useful in various applications, such as network analysis and computer science, where it helps in understanding the structure and connectivity of networks. For example, in a communication network, an eingängig graph might represent a situation where only one node is connected to the rest of the network by a single link, which could be a point of failure or vulnerability.

In summary, eingängigkeit refers to the presence of exactly one vertex with a degree of one in a graph. This concept is significant in graph theory and has practical applications in network analysis and computer science.