On which of the following statements does the time complexity of checking if an edge exists between two particular vertices is not, depends?Group of answer choicesIs independent of both the number of edges and verticesDepends on the number of edgesDepends on the number of verticesIt depends on both the number of edges and vertices

The time complexity of checking if an edge exists between two particular vertices in a graph can depend on the data structure used to represent the graph.

1. If the graph is represented using an adjacency matrix (a 2D array), then the time complexity is O(1), because we can directly access the cell that represents the edge between the two vertices. This is independent of both the number of edges and vertices.

2. If the graph is represented using an adjacency list (a list of lists), then the time complexity can be O(V) in the worst case, where V is the number of vertices. This is because we may need to traverse all the vertices in the worst case.

3. If the graph is represented using an edge list (a list of pairs of vertices), then the time complexity can be O(E) in the worst case, where E is the number of edges. This is because we may need to traverse all the edges in the worst case.

So, the time complexity of checking if an edge exists between two particular vertices can be independent of both the number of edges and vertices, can depend on the number of vertices, or can depend on the number of edges, depending on the data structure used to represent the graph. It does not necessarily depend on both the number of edges and vertices at the same time.