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If GGG is a graph with 61 vertices and 60 edges, then:
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Find the 10×1010 \times 1010×10 adjacency matrix AAA of the graph above.
Input det((A2+A−K)2) \det \left( \frac{( A^2 + A - K )}{2} \right) det(2(A2+A−K)) as your answer.
Details and assumptions
Which of the following adjacency matrices represent a bipartite graph?
A=(0110010010100000100100010),B=(0101010101010101010101010) \text{A} = \left(\begin{array}{ccccc}0 & \color{#D61F06}{1} & \color{#D61F06}{1} & 0 & 0 \\ \color{#D61F06}{1} & 0 & 0 & \color{#D61F06}{1} & 0 \\\color{#D61F06}{1} & 0 & 0 & 0 & 0 \\0 & \color{#D61F06}{1} & 0 & 0 & \color{#D61F06}{1} \\0 & 0 & 0 & \color{#D61F06}{1} & 0\end{array}\right), \quad \text{B} = \left(\begin{array}{ccccc}0 & \color{#3D99F6}{1} & 0 & \color{#3D99F6}{1}& 0 \\ \color{#3D99F6}{1} & 0 & \color{#3D99F6}{1} & 0 & \color{#3D99F6}{1} \\0 & \color{#3D99F6}{1} & 0 & \color{#3D99F6}{1} & 0 \\ \color{#3D99F6}{1} & 0 & \color{#3D99F6}{1} & 0 & \color{#3D99F6}{1} \\0 & \color{#3D99F6}{1} & 0 & \color{#3D99F6}{1} & 0\end{array}\right) A=⎝⎜⎜⎜⎜⎛0110010010100000100100010⎠⎟⎟⎟⎟⎞,B=⎝⎜⎜⎜⎜⎛0101010101010101010101010⎠⎟⎟⎟⎟⎞
C=(0010000100110110010000100) \text{C} = \left(\begin{array}{ccccc}0 & 0 & \color{#20A900}{1} & 0 & 0 \\0 & 0 & \color{#20A900}{1} & 0 & 0 \\\color{#20A900}{1} & \color{#20A900}{1} & 0 & \color{#20A900}{1} & \color{#20A900}{1} \\0 & 0 & \color{#20A900}{1} & 0 & 0 \\0 & 0 & \color{#20A900}{1} & 0 & 0\end{array}\right)C=⎝⎜⎜⎜⎜⎛0010000100110110010000100⎠⎟⎟⎟⎟⎞
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