The number of elements in the adjacency matrix of a graph having 7 vertices is __________Marks : 1Negative Marks : 0Answer here1449736

To determine the number of elements in the adjacency matrix of a graph with 7 vertices, we can follow these steps:

1. ### Break Down the Problem

The adjacency matrix represents all possible connections (edges) between the vertices in a graph. For a graph with $n$ vertices, the adjacency matrix will be of size $n \times n$.

2. ### Relevant Concepts

• An adjacency matrix for a graph with $n$ vertices contains $n^2$ elements.
• In the case of undirected graphs, the adjacency matrix is symmetric, while in directed graphs, it is not necessarily symmetric.

3. ### Analysis and Detail

• For a graph with $n = 7$ vertices, the adjacency matrix will have dimensions $7 \times 7$.
• Thus, the number of elements in the adjacency matrix can be calculated as: $\text{Number of elements} = n \times n = 7 \times 7 = 49$

4. ### Verify and Summarize

We calculated the number of elements to be $49$. Since the matrix has dimensions equal to the number of vertices squared, our solution is consistent with the properties of adjacency matrices.

Final Answer

The number of elements in the adjacency matrix of a graph having 7 vertices is 49.