vertexinduced
In graph theory, a vertex-induced subgraph on a set S of vertices of a graph G=(V,E) is the subgraph G[S] that contains all and only the edges of G whose endpoints lie in S. Equivalently, G[S] has vertex set S and edge set E[S] = { (u,v) ∈ E : u ∈ S and v ∈ S }. In directed graphs, the induced subgraph preserves the direction of each edge.
The vertex-induced subgraph is obtained by deleting from G all vertices not in S and all edges
Interpretations and examples: The induced subgraph reflects the induced relationships among the chosen vertices. For instance,
Distinctions and scope: Induced subgraphs are distinguished from arbitrary subgraphs that can omit some edges among
Applications: Induced subgraphs are fundamental in structural graph theory, property testing, and algorithm design. They are