In graph theory, what is the term for a set of vertices with no edges connecting them?Group of answer choicesComponentPathIsolateDegree

In graph theory, the term for a set of vertices with no edges connecting them is commonly referred to as an "Isolate" or "Isolated Vertices." Isolated vertices are those that have no connections to any other vertices within the graph.

Here’s a brief explanation of the other terms provided in your choices:

1. Component: This term generally refers to a connected subgraph of a graph, meaning that there is at least one path between any two vertices within that component.

2. Path: A path in graph theory is a sequence of vertices where each adjacent pair is connected by an edge.

3. Degree: The degree of a vertex is the number of edges incident to the vertex. For isolated vertices, the degree is zero since there are no edges connected to them.

Therefore, the correct term from your choices for a set of vertices with no edges connecting them is Isolate.