6.4.6 Graph theory

Problem: Given a weight matrix $\mathrm{\Omega }$ 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. $$\left(\begin{array}{cccccc}-& 2& \mathrm{\infty }& 3& 4& \mathrm{\infty }\\ \mathrm{\infty }& -& 6& \mathrm{\infty }& \mathrm{\infty }& \mathrm{\infty }\\ \mathrm{\infty }& \mathrm{\infty }& -& \mathrm{\infty }& \mathrm{\infty }& 2\\ \mathrm{\infty }& 2& 4& -& 3& 7\\ \mathrm{\infty }& 7& 5& \mathrm{\infty }& -& 10\\ \mathrm{\infty }& \mathrm{\infty }& \mathrm{\infty }& \mathrm{\infty }& \mathrm{\infty }& \mathrm{\infty }\end{array}\right).$$