Graphs: Level 3 Challenges

     

If GG is a graph with 61 vertices and 60 edges, then:

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Thaddeus Abiy by Thaddeus Abiy

Find the 10×1010 \times 10 adjacency matrix AA of the graph above.

Input det⁡((A2+A−K)2) \det \left( \frac{( A^2 + A - K )}{2} \right) as your answer.

Details and assumptions

  • KK is the 10×1010 \times 10 matrix which has 11 for all entries.
Thaddeus Abiy by Thaddeus Abiy

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)

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)

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Pranshu Gaba by Pranshu Gaba
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