6.4.6 Graph theory

Problem: Given a weight matrix \( \Omega \) of graph \( G \). find the value of the minimum path and the path itself from vertex \( v_{1} \) to vertex \( v_{6} \) using Dijkstra's algorithm, and then the value of the maximum path and the path itself between the same vertices. \[ \left(\begin{array}{cccccc} - & 2 & \infty & 3 & 4 & \infty \\ \infty & - & 6 & \infty & \infty & \infty \\ \infty & \infty & - & \infty & \infty & 2 \\ \infty & 2 & 4 & - & 3 & 7 \\ \infty & 7 & 5 & \infty & - & 10 \\ \infty & \infty & \infty & \infty & \infty & \infty \end{array}\right) . \]