Description: In graph theory, the term ‘boundary’ refers to the set of vertices that are adjacent to a specific subgraph but do not belong to it. This notion is fundamental for understanding the structure and properties of graphs, as it allows for the identification of how different parts of a graph are connected and how a subgraph can be expanded. The boundary acts as a limit that separates the subgraph from the rest of the graph, and its analysis can provide valuable information about connectivity and the overall structure of the graph. Additionally, the boundary can be used to study properties such as graph expansion, where the number of boundary vertices that can be reached from the subgraph is evaluated. In practical applications, identifying the boundary is crucial in optimization problems, communication networks, and social network analysis, where interactions between different groups or components are sought to be understood. In summary, the boundary is a key concept that helps to decompose and analyze the complexity of graphs, facilitating the understanding of their characteristics and behaviors.
