Suppose you are given a weighted graph with vertices labeled from A to E. After completely performing the Dijkstra's Algorithm, you have the following permanent labels. What is the shortest path form A to D? P(A) = 04, P(B) = Р (В) %3D ЗА, Р(C) 3 14, Р(D) %3D Зс, 2 C → D А — D A → B → E –→ D А— С— D

Choose the best answer. An algorithm to determine if a graph with n=>3 vertices is a star is: a.Pick any node; if its degree is 1, traverse to a neighbor node. Consider the node you end up with. If its degree is not n-1, return false, else check that all its neighbors have degree 1: if so, return true, else return false. b.Pick any node; if its degree is n-1, traverse to a neighbor node. Consider the node you end up with. If its degree is not 1, return true, else check that all its neighbors have degree n-1: if so, return true, else return false. c.Pick any node; if its degree is 3, traverse to a neighbor node. Consider the node you end up with. If its degree is not n-1, return false, else check that all its neighbors have degree 3: if so, return true, else return false. d. Pick any node; if its degree is n-3, traverse to a neighbor node. Consider the node you end up with. If its degree is not n-3, return true, else check that all its neighbors have degree 3: if so, return false,…

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

Consider a graph where vertices represent intersections and edges represent roads. The company Food To Go can place a maximum of one food cart at each intersection. A food cart placed at intersection X has an income equal to the number of roads at intersection X (ie, the degree of vertex X). If two food carts share a road, the income of that road is shared equally among the two. We are interested in calculating the total profit of all food carts placed, ie, the total income minus the cost, where each food cart costs 1 unit and each road provides an income of 1 unit. More formally, the profit for a graph G = (V, E) where the set SC V represents food cart locations, is calculated by the number of edges covered by the vertices in S minus the size of S (ie. |S). A D C E B In this example, placing a food cart on each of the vertices A and C will result in a profit of ISCA P (A D(CD) (CFU VACU-5

Draw a graph G containing the following vertices and edges. V(G) = {0, 1, 2, 3, 4, 5, 6} E(G) = { (0, 1), (0, 2), (0, 3), (2, 1), (2, 4), (5, 1), (5, 3)}

Given an undirected, weighted graph G(V, E) with n vertices and m edges, design an (O(m + n)) algorithm to compute a graph G1 (V, E1 ) on the same set of vertices, where E1 subset of  E and E1 contains the k edges with the smallest edge weights , where k < m.

Algorithms

Consider the following edge-weighted graph G with 9 vertices and 16 edges: 90 Q6.1 Kruskal 40 50 80 130 110 70 S 150 60 30 10 120 140 20 100 List the weights of the MST edges in the order that Kruskal's algorithm adds them the MST. Your answer should be a sequence of 8 integers, with one space between each integer, 14

Consider a graph with five nodes labeled A, B, C, D, and E. Let's say we have the following edges with their weights: A to B with weight 3 A to C with weight 1 B to C with weight 2 B to D with weight 1 C to E with weight 4 D to E with weight 2 a. Find the shortest path from A to E using Dijkstra's algorithm. (Draw the finished shortest path) b. Use Prim to find the MST (Draw the finished MST) c. Use Kruskal to find the MST (Draw the finished MST) d. What's the difference between Prim and Kruskal algorithms? Do they always have the same result? Why or why not.

Consider a graph with five nodes labeled A, B, C, D, and E. Let's say we have the following edges with their weights: A to B with weight 3 A to C with weight 1 B to C with weight 3 B to D with weight 1 C to E with weight 4 D to E with weight 2 a. Find the shortest path from A to E using Dijkstra's algorithm   (Would anything change if B to C weight was changed from 3 to 4? To 1? What about 5?)