Which of the following statements about Adjacency Matrices are true? Note: You may select multiple answers. Group of answer choices Adjacency matrices are symmetric for both directed and undirected graphs. An adjacency matrix for a graph with V vertices requires O(V2) space, irrespective of the number of edges in the graph. Finding the existence of an edge in a graph given an adjacency matrix representation is an O(1) operation. Finding the neighbours of a vertex v, in a graph of V vertices, given its adjacency matrix representation is a Ө(V2) operation.

Here are the correct statements:

1. An adjacency matrix for a graph with V vertices requires O(V^2) space, irrespective of the number of edges in the graph.

Explanation: An adjacency matrix is a square matrix with dimensions V x V, where V is the number of vertices in the graph. Therefore, it requires O(V^2) space.

2. Finding the existence of an edge in a graph given an adjacency matrix representation is an O(1) operation.

Explanation: In an adjacency matrix, the existence of an edge between two vertices can be determined by accessing the cell at the intersection of the row and column corresponding to the two vertices. This is a constant time operation, hence O(1).

The following statements are incorrect:

1. Adjacency matrices are symmetric for both directed and undirected graphs.

Explanation: This is only true for undirected graphs. For directed graphs, the adjacency matrix is not necessarily symmetric because the existence of an edge from vertex i to vertex j does not guarantee an edge from vertex j to vertex i.

2. Finding the neighbours of a vertex v, in a graph of V vertices, given its adjacency matrix representation is a Ө(V^2) operation.

Explanation: This operation is actually O(V), not O(V^2). To find the neighbors of a vertex, we only need to scan the row (or column, depending on the convention used) corresponding to that vertex in the adjacency matrix. Since there are V elements in a row (or column), this operation is O(V).