Find the vertex matrix of the following graphs.
The vertex matrix of a graph is such that:
- a_{i,j}=1 if there is directed edge from vertex i to vertex j.
- a_{i,j}=0 if there is no directed edge going from vertex i to vertex j.
The given graph is:
The graph gives:
- Entries a_{1{,}4} , a_{1{,}5}, a_{2{,}4}, a_{3{,}4}, a_{4{,}1}, a_{4{,}5}, a_{5{,}6}, and a_{6{,}3} as 1.
- All other entries equal 0.
The vertex matrix is \begin{pmatrix} 0 & 0 & 0 & 1 &1&0 \cr\cr 0& 0& 0& 1 &0 &0 \cr\cr 0 & 0 & 0 & 1 &0 & 0 \cr\cr 1 & 0 & 0 & 0 & 1 & 0 \cr\cr 0 & 0 & 0 & 0 & 1 & 0 \cr\cr 0 & 0 & 1 & 0 & 0 & 0 \end{pmatrix}
The vertex matrix of a graph is such that:
- a_{i,j}=1 if there is directed edge from vertex i to vertex j.
- a_{i,j}=0 if there is no directed edge going from vertex i to vertex j.
The graph gives:
- Entries a_{1{,}4} , a_{1{,}5}, a_{2{,}3}, and a_{2{,}5} as 1.
- All other entries equal 0.
The vertex matrix is \begin{pmatrix} 0 & 0 & 0 & 1 &1 \cr\cr 0& 0& 1& 0 &1 \cr\cr 0 & 0 & 0 & 0&0 \cr\cr 0 & 0 & 0 & 0 & 0 \cr\cr 0 & 0 & 0 & 0 & 0 \end{pmatrix}
The vertex matrix of a graph is such that:
- a_{i,j}=1 if there is directed edge from vertex i to vertex j.
- a_{i,j}=0 if there is no directed edge going from vertex i to vertex j.
The graph gives:
- Entries a_{1{,}4} , a_{1{,}5}, a_{2{,}3}, a_{2{,}5}, a_{3{,}6}, a_{5{,}2}, and a_{6{,}3} as 1.
- All other entries equal 0.
The vertex matrix is \begin{pmatrix} 0 & 0 & 0 & 1 &1&0 \cr\cr 0& 0& 1& 0 &1 &0 \cr\cr 0 & 0 & 0 & 0 &0 & 1 \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}
The vertex matrix of a graph is such that:
- a_{i,j}=1 if there is directed edge from vertex i to vertex j.
- a_{i,j}=0 if there is no directed edge going from vertex i to vertex j.
The graph gives:
- Entries a_{1{,}4} , a_{1{,}5}, a_{2{,}3}, a_{2{,}5}, a_{3{,}6}, a_{4{,}5}, a_{5{,}2}, a_{5{,}2}, a_{5{,}4}, a_{5{,}6}, a_{6{,}3}, and a_{6{,}5} as 1.
- All other entries equal 0.
The vertex matrix is \begin{pmatrix} 0 & 0 & 0 & 1 &1&0 \cr\cr 0& 0& 1& 0 &1 &0 \cr\cr 0 & 0 & 0 & 0 &0 & 1 \cr\cr 0 & 0 & 0 & 0 & 1 & 0 \cr\cr 0 & 1 & 0 & 1 & 0 & 1 \cr\cr 0 & 0 & 1 & 0 & 1 & 0 \end{pmatrix}
The vertex matrix of a graph is such that:
- a_{i,j}=1 if there is directed edge from vertex i to vertex j.
- a_{i,j}=0 if there is no directed edge going from vertex i to vertex j.
The graph gives:
- Entries a_{1{,}2} , a_{1{,}3}, a_{2{,}4}, and a_{3{,}4} as 1.
- All other entries equal 0.
The vertex matrix is \begin{pmatrix} 0 & 1 & 1 & 0 \cr\cr 0 & 0 & 0& 1 \cr\cr 0 & 0 & 0 & 1 \cr\cr 0 & 0 & 0 & 0 \end{pmatrix}.
The vertex matrix of a graph is such that:
- a_{i,j}=1 if there is directed edge from vertex i to vertex j.
- a_{i,j}=0 if there is no directed edge going from vertex i to vertex j.
The graph gives:
- Entries a_{1{,}2} , a_{1{,}3}, a_{2{,}1}, a_{2{,}4}, a_{3{,}1}, a_{3{,}4}, a_{4{,}2}, and a_{4{,}3} as 1.
- All other entries equal 0.
The vertex matrix is \begin{pmatrix} 0 & 1 & 1 & 0 \cr\cr 1 & 0 & 0 & 1 \cr\cr 1 & 0 & 0 & 1 \cr\cr 0 & 1 & 1 & 0 \end{pmatrix}
The vertex matrix of a graph is such that:
- a_{i,j}=1 if there is directed edge from vertex i to vertex j.
- a_{i,j}=0 if there is no directed edge going from vertex i to vertex j.
The graph gives:
- Entries a_{1{,}4} , a_{1{,}2}, a_{2{,}3}, a_{2{,}5}, a_{3{,}6}, a_{4{,}5}, and a_{5{,}6} as 1.
- All other entries equal 0.
The vertex matrix is:
\begin{pmatrix} 0 & 1 & 0 & 1 &0&0 \cr\cr 0& 0& 1& 0 &1 &0 \cr\cr 0 & 0 & 0 & 0 &0 & 1 \cr\cr 0 & 0 & 0 & 0 & 1 & 0 \cr\cr 0 & 0 & 0 & 0 & 0 & 1 \cr\cr 0 & 0 & 0 & 0 & 0 & 0 \end{pmatrix}