Find the graph that matches the following vertex matrix.
\begin{pmatrix} 0 & 1 & 1 & 1 \cr\cr 0 & 0 & 1 & 0 \cr\cr 1 & 0 & 0 & 1 \cr\cr 1 & 1 & 1 & 0 \end{pmatrix}
An nxn matrix represents a graph with n vertices.
- If a_{i,j}=1, then there is a directed edge from vertex i to vertex j.
- If a_{i,j}=0, then there is no directed edge from vertex i to vertex j.
The matrix is:
\begin{pmatrix} 0 & 1 & 1 & 1 \cr\cr 0 & 0 & 1 & 0 \cr\cr 1 & 0 & 0 & 1 \cr\cr 1 & 1 & 1 & 0 \end{pmatrix}
Therefore, the graph uses only four vertices.
There are directed edges from vertex:
- 1 to 2
- 1 to 3
- 1 to 4
- 2 to 3
- 3 to 1
- 3 to 4
- 4 to 1
- 4 to 2
- 4 to 3
The graph is:
\begin{pmatrix} 0 & 1 & 1 & 1 \cr\cr 1 & 0 & 1 & 1 \cr\cr 1 & 1 & 0 & 1 \cr\cr 1 & 1 & 1 & 0 \end{pmatrix}
An nxn matrix represents a graph with n vertices.
- If a_{i,j}=1, then there is a directed edge from vertex i to vertex j.
- If a_{i,j}=0, then there is no directed edge from vertex i to vertex j.
The matrix is:
\begin{pmatrix} 0 & 1 & 1 & 1 \cr\cr 1 & 0 & 1 & 1 \cr\cr 1 & 1 & 0 & 1 \cr\cr 1 & 1 & 1 & 0 \end{pmatrix}
Therefore, the graph uses only four vertices.
There are directed edges from vertex:
- 1 to 2
- 1 to 3
- 1 to 4
- 2 to 1
- 2 to 3
- 2 to 4
- 3 to 1
- 3 to 2
- 3 to 4
- 4 to 1
- 4 to 2
- 4 to 3
\begin{pmatrix} 0 & 0 & 0 & 0 \cr\cr 0 & 0 & 0 & 0 \cr\cr 0 & 0 & 0 & 0 \cr\cr 0 & 1 & 1 & 0 \end{pmatrix}
An nxn matrix represents a graph with n vertices.
- If a_{i,j}=1, then there is a directed edge from vertex i to vertex j.
- If a_{i,j}=0, then there is no directed edge from vertex i to vertex j.
The matrix is:
\begin{pmatrix} 0 & 0 & 0 & 0 \cr\cr 0 & 0 & 0 & 0 \cr\cr 0 & 0 & 0 & 0 \cr\cr 0 & 1 & 1 & 0 \end{pmatrix}
Therefore, the graph uses only four vertices.
There are directed edges from vertex:
- 4 to 2
- 4 to 3
\begin{pmatrix} 0 & 1 & 1 & 1 &1 &0 \cr\cr 0 & 0 & 1 & 0 &1 &1 \cr\cr 1 & 0 & 0 & 1&0&0 \cr\cr 1 & 1 & 1 & 0 &0&0 \cr \cr 1&1&1&0&0&0 \cr \cr 1&1&1&0&0&0\end{pmatrix}
An nxn matrix represents a graph with n vertices.
- If a_{i,j}=1, then there is a directed edge from vertex i to vertex j.
- If a_{i,j}=0, then there is no directed edge from vertex i to vertex j.
The matrix is:
\begin{pmatrix} 0 & 1 & 1 & 1 &1 &0 \cr\cr 0 & 0 & 1 & 0 &1 &1 \cr\cr 1 & 0 & 0 & 1&0&0 \cr\cr 1 & 1 & 1 & 0 &0&0 \cr \cr 1&1&1&0&0&0 \cr \cr 1&1&1&0&0&0\end{pmatrix}
Therefore, the graph uses only six vertices.
There are directed edges from vertex:
- 1 to 2
- 1 to 3
- 1 to 4
- 1 to 5
- 2 to 3
- 2 to 5
- 2 to 6
- 3 to 1
- 3 to 4
- 4 to 1
- 4 to 2
- 4 to 3
- 5 to 1
- 5 to 2
- 5 to 3
- 6 to 1
- 6 to 2
- 6 to 3
\begin{pmatrix} 0 & 0 & 0 & 0 &0 &0 \cr\cr 0 & 0 & 0 & 0 &0 & 0\cr\cr 0 & 0 & 0 & 0&0&0 \cr\cr 0 & 0 & 0 & 0 &0&0 \cr \cr 0&1&0&0&0&0 \cr \cr 0&0&1&0&0&0\end{pmatrix}
An nxn matrix represents a graph with n vertices.
- If a_{i,j}=1, then there is a directed edge from vertex i to vertex j.
- If a_{i,j}=0, then there is no directed edge from vertex i to vertex j.
The matrix is:
\begin{pmatrix} 0 & 0 & 0 & 0 &0 &0 \cr\cr 0 & 0 & 0 & 0 &0 & 0\cr\cr 0 & 0 & 0 & 0&0&0 \cr\cr 0 & 0 & 0 & 0 &0&0 \cr \cr 0&1&0&0&0&0 \cr \cr 0&0&1&0&0&0\end{pmatrix}
Therefore, the graph uses only six vertices.
There are directed edges from vertex:
- 5 to 2
- 6 to 3
\begin{pmatrix} 0 & 1 & 1 \cr\cr 1 & 0 & 1 \cr\cr 1 & 1 & 0 \end{pmatrix}
An nxn matrix represents a graph with n vertices.
- If a_{i,j}=1, then there is a directed edge from vertex i to vertex j.
- If a_{i,j}=0, then there is no directed edge from vertex i to vertex j.
The matrix is:
\begin{pmatrix} 0 & 1 & 1 \cr\cr 1 & 0 & 1 \cr\cr 1 & 1 & 0 \end{pmatrix}
Therefore, the graph uses only six vertices.
There are directed edges from vertex:
- 1 to 2
- 1 to 3
- 2 to 1
- 2 to 3
- 3 to 1
- 3 to 2
\begin{pmatrix} 0 & 1 \cr\cr 1 & 0 \end{pmatrix}
An nxn matrix represents a graph with n vertices.
- If a_{i,j}=1, then there is a directed edge from vertex i to vertex j.
- If a_{i,j}=0, then there is no directed edge from vertex i to vertex j.
The matrix is:
\begin{pmatrix} 0 & 1 \cr\cr 1 & 0 \end{pmatrix}
Therefore, the graph uses only two vertices.
There are directed edges from vertex:
- 1 to 2
- 2 to 1
