Description: A boundary vertex is a fundamental concept in graph theory, referring to those vertices that belong to the boundary of a specific subgraph. In more technical terms, a boundary vertex is one that is connected to at least one vertex that does not belong to the subgraph in question. This characteristic distinguishes it from internal vertices, which are completely surrounded by other vertices of the same subgraph. Identifying boundary vertices is crucial in various applications, as it helps to better understand the structure and properties of graphs. For example, in network analysis, boundary vertices can represent critical connection points between different communities or groups within the graph. Additionally, studying these vertices can help optimize routes and flows in various systems. In summary, boundary vertices are essential for analyzing and understanding the topology of graphs, as well as for solving practical problems in various disciplines, including computer science, biology, and sociology.
