Run Dijkstra's algorithm on the following graph, starting from vertex A. Whenever there are multiple choices of vertex at the same time, choose the one that is alphabetically first. You are expected to show how you initialize the graph, how you picked a vertex and update the d values at the each, and what is final shortest distance of each vertex from A. B A F E

In the following graph, find all the shortest paths from vertex "a" to all the other vertices.

Q7: Run the Ford-Fulkerson algorithm on the graph assigned to you and determine the maximum flow possible between the source (s) and destination (d) as well as determine the minimum cut of edges (set of edges with the minimum sum of the edge weights) to disconnect the source and destination. Show all the work (including the use of the residual graphs in each iteration).

Implement Dijkstra's algorithm to find the shortest path between two nodes in a graph. What is the time complexity of your solution?

Using Dijkstra’s algorithm, find the shortest path between C and all other vertices. Write the  python algorithm for it.

We have the following directed graph G, where the number on each edge is the cost of the edge. 1. Step through Dijkstra’s Algorithm on the graph starting from vertex s, and complete the table below to show what the arrays d and p are at each step of the algorithm. For any vertex x, d[x] stores the current shortest distance from s to x, and p[x] stores the current parent vertex of x. 2. After you complete the table, provide the returned shortest path from s to t and the cost of the path.

A B. D H Suppose you run the topological sort algorithm on the graph above starting at vertex C. Use the rule that when there is a choice of vertices for the algorithm to visit, it visits them in alphabetic order. Which vertex would end up first in the eventual topologically sorted order? Which would end up being second? Which would end up being third? Which would end up being fourth? Which would end up being fifth? Which would end up being sixth?

Run BFS algorithm on the following graph starting with vertex s. Whenever there is a choice of vertices, choose the one that is alphabetically first. What is the order that the vertices are visited? What is the shortest path from vertex s to vertex b?

Given a graph that is a tree (connected and acyclic). (1) Pick any vertex v. (II) Compute the shortest path from v to every other vertex. Let w be the vertex with the largest shortest path distance. (III) Compute the shortest path from w to every other vertex. Let x be the vertex with the largest shortest path distance. Consider the path p from w to x. Which of the following are true a. p is the longest path in the graph b. p is the shortest path in the graph c. p can be calculated in time linear in the number of edges/vertices a,c a,b a,b,c b.c

Draw the adjacency list for the given undirected graph. No need for any program or something.