The number of distinct minimum spanning trees for the weighted graph below is ________

Consider the directed graph shown in the figure below. There are multiple shortest paths between vertices S and T. Which one will be reported by Dijkstra’s shortest path algorithm? Assume that, in any iteration, the shortest path to a vertex v is updated only when a strictly shorter path to v is discovered.

An undirected graph G(V, E) contains n ( n > 2 ) nodes named v₁ , v₂ ,….v_n. Two nodes v_i , v_j are connected if and only if 0 < |i – j| <= 2. Each edge (v_i, v_j ) is assigned a weight i + j. A sample graph with n = 4 is shown below. What will be the cost of the minimum spanning tree (MST) of such a graph with n nodes?

An undirected graph G(V, E) contains n ( n > 2 ) nodes named v₁ , v₂ ,….v_n. Two nodes v_i , v_j are connected if and only if 0 < |i – j| <= 2. Each edge (v_i, v_j ) is assigned a weight i + j. A sample graph with n = 4 is shown below. The length of the path from v5 to v6 in the MST of previous question with n = 10 is