5.4 Shortest-path problem Let G=(v,E, w) be a weighted connected simple graph, w is a function from edges set E to position real numbers set. We denoted the weighted of edge i, by w(i,j, and w(i,j)=+oo when JEE 4 Definition 21: Let the length of a path p in a weighted graph G=(V,E, w) be the sum of the weights of the edges of this path. We denoted by w(p). The distance between two vertices u and v is the length of a shortest path between u and v, we denoted by d(u, v). u=y min w(p)l pis a path between u and v, there is a path between u and v P5.4 Shortest-path problem ❖ Let G=(V,E,w) be a weighted connected simple graph, w is a function from edges set E to position real numbers set. We denoted the weighted of edge {i,j} by w(i,j), and w(i,j)=+ when {i,j}E ❖ Definition 21: Let the length of a path p in a weighted graph G =(V,E,w) be the sum of the weights of the edges of this path. We denoted by w(p). The distance between two vertices u and v is the length of a shortest path between u and v, we denoted by d(u,v).     = = w p p is a path between u and v there is a path between u and v u v d u v p min { ( )| } 0 ( , )