# Thread: discrete math help logic

1. ## discrete math help logic

ive been looking for help on this question for some time can someone plz help me

2. Hello, srk619!

I can help with the first two parts . . .

(a) Draw the graph with this adjacency matrix:

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

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

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

. - . - . - . . . $\displaystyle ^{\downarrow}$
$\displaystyle A^2 \;=\;\begin{bmatrix} 2&1& {\color{red}\boxed{1}} &1&0&0 \\ 1&2&1&1&0&0 \\ 1&0&3&0&1&1 \\ 1&1&0&3&1&1 \\ 0&0&1&1&2&1 \\ 0&0&1&1&1&2\end{bmatrix}$