discrete math help logic

• February 23rd 2009, 02:58 AM
srk619
discrete math help logic
ive been looking for help on this question for some time can someone plz help me
• February 23rd 2009, 05:27 AM
Soroban
Hello, srk619!

I can help with the first two parts . . .

Quote:

(a) Draw the graph with this adjacency matrix:

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

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

Quote:

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

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