Question

consider the given network. write the given network in matrix form.

\\( a = \

$$\begin{bmatrix} 0 & 1 & 1 \\\\ 1 & 1 & 0 \\\\ 1 & 0 & 0 \\end{bmatrix}$$

\\)

\\( a = \

$$\begin{bmatrix} 0 & 1 & 1 \\\\ 1 & 0 & 0 \\\\ 1 & 0 & 0 \\end{bmatrix}$$

\\)

Explanation:

Identify vertices and connections

The network consists of three vertices: \(P\), \(Q\), and \(R\).
The connections (edges) between them are:

• Between \(P\) and \(Q\)
• Between \(P\) and \(R\)

There is no connection between \(Q\) and \(R\), and no self-loops.

Construct the adjacency matrix

Using the alphabetical order of vertices \(P\), \(Q\), and \(R\) for rows and columns:

• Row 1 (\(P\)): connects to \(Q\) and \(R\). Elements: \([0, 1, 1]\)
• Row 2 (\(Q\)): connects to \(P\). Elements: \([1, 0, 0]\)
• Row 3 (\(R\)): connects to \(P\). Elements: \([1, 0, 0]\)

Match with options

The resulting adjacency matrix is:

$$ A =
LATEXBLOCK0
$$

This matches the second visible option.

Answer:

• (A) \(A =

$$\begin{bmatrix} 0 & 1 & 1 \\ 1 & 1 & 0 \\ 1 & 0 & 0 \end{bmatrix}$$

\)

• **(B) \(A =

$$\begin{bmatrix} 0 & 1 & 1 \\ 1 & 0 & 0 \\ 1 & 0 & 0 \end{bmatrix}$$

\) (Correct answer)**