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Math Help - discrete math help logic

  1. #1
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    discrete math help logic

    ive been looking for help on this question for some time can someone plz help me
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  2. #2
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    Hello, srk619!

    I can help with the first two parts . . .



    (a) Draw the graph with this adjacency matrix:

    . . . . . A \;=\;\begin{bmatrix}0&1&1&0&0&0 \\ 1&0&1&0&0&0 \\ 1&1&0&1&0&0 \\ 0&0&1&0&1&1 \\ 0&0&0&1&0&1 \\ 0&0&0&1&1&0 \end{bmatrix}

    . . . . . . . . . . \begin{array}{cccccc}<br />
& & \boxed{2} \\<br />
& \nearrow\!\!\swarrow & & \searrow\!\!\nwarrow \\<br />
\boxed{1} &\leftrightarrows & \leftrightarrows & \leftrightarrows& \boxed{3} \\ \\[-3mm]<br />
& & & & \uparrow\downarrow \\ \\[-3mm]<br />
\boxed{6} & \leftrightarrows & \leftrightarrows & \leftrightarrows& \boxed{4} \\<br />
& \searrow\!\!\nwarrow & & \nearrow\!\!\swarrow \\<br />
& & \boxed{5} \end{array}



    (b) Calculate A^2 and hence say many paths of length 2
    there are between vertex 1 and vertex 3.

    . - . - . - . . . ^{\downarrow}
    A^2 \;=\;\begin{bmatrix} 2&1& {\color{red}\boxed{1}} &1&0&0 \\<br />
1&2&1&1&0&0 \\ 1&0&3&0&1&1 \\ 1&1&0&3&1&1 \\ 0&0&1&1&2&1 \\ 0&0&1&1&1&2\end{bmatrix}

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