Graphs
by
Thaddeus Abiy
Input \( \det \left( \frac{( A^2 + A - K )}{2} \right) \) as your answer.
Details and assumptions
- \(K\) is the \(10 \times 10\) matrix which has \(1\) for all entries.
by
Thaddeus Abiy
Which of the following adjacency matrices represent a bipartite graph?
\[ \text{A} = \left(\begin{array}{ccccc}0 & \color{red}{1} & \color{red}{1} & 0 & 0 \\ \color{red}{1} & 0 & 0 & \color{red}{1} & 0 \\\color{red}{1} & 0 & 0 & 0 & 0 \\0 & \color{red}{1} & 0 & 0 & \color{red}{1} \\0 & 0 & 0 & \color{red}{1} & 0\end{array}\right), \quad \text{B} = \left(\begin{array}{ccccc}0 & \color{blue}{1} & 0 & \color{blue}{1}& 0 \\ \color{blue}{1} & 0 & \color{blue}{1} & 0 & \color{blue}{1} \\0 & \color{blue}{1} & 0 & \color{blue}{1} & 0 \\ \color{blue}{1} & 0 & \color{blue}{1} & 0 & \color{blue}{1} \\0 & \color{blue}{1} & 0 & \color{blue}{1} & 0\end{array}\right) \]
\[ \text{C} = \left(\begin{array}{ccccc}0 & 0 & \color{green}{1} & 0 & 0 \\0 & 0 & \color{green}{1} & 0 & 0 \\\color{green}{1} & \color{green}{1} & 0 & \color{green}{1} & \color{green}{1} \\0 & 0 & \color{green}{1} & 0 & 0 \\0 & 0 & \color{green}{1} & 0 & 0\end{array}\right)\]
by
Pranshu Gaba