Using the graph below, if we apply Dijkstra's algorithm to find the shortest distance between node A and all the others, in what order do the the visited set (i.e their distances have been finalized)? E Select one: O a. CBEGFD O b. CBEFGD O c. BCGEFD O d. BCFGED

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

4-Clique Problem The clique problem is to find cliques in a graph. A clique is a set of vertices that are all adjacent - connected - to each other. A 4-clique is a set of 4 vertices that are all connected to each other. So in this example of the 4-Clique Problem, we have a 7-vertex graph. A brute-force algorithm has searched every possible combination of 4 vertices and found a set that forms a clique: https://en.wikipedia.org/wiki/Clique_problem   You should read the Wikipedia page for the Clique Problem (and then read wider if need be) if you need to understand more about it. Note that the Clique Problem is NP-Complete and therefore when the graph size is large a deterministic search is impractical. That makes it an ideal candidate for an evolutionary search. For this assignment you must suppose that you have been tasked to implement the 4-clique problem as an evolutionary algorithm for any graph with any number of vertices (an n-vertex graph). The algorithm succeeds if it finds a…

Kruskal's minimum spanning tree algorithm is executed on the following graph. Select all edges from edgeList that belong to the minimum spanning tree. edgeList result List AD BC BE CF EF DG EG EH GH D 7 9 G 1 B 5 3 A E H 4 2 6 8 F

1. Input: An undirected weighted graph G = (V, E, w)2. Output: An MST T = (V, E) of G3. T ← Ø4. Sort edges of G in non-increasing order and place them in a queue Q.5. repeat6. Remove the first edge (u, v) from Q and add it to T if it does not form a cyclewith the edges edge that are already included in T .7. until there are n − 1 edges in T .We can use union-find data structure to find whether the two endpoints of theselected edge are in the same set (the current MST fragment). It can be shown thatthis algorithm is correct and has a time complexity of O(m log n) [1].Give Python Implementation of algo

Consider the graph below above. Use Kruskal's algorithm to find the minimum spanning tree. List the weights of the selected edges separated by commas in the order of selection.

Kruskal's algorithm is a minimum-spanning-tree algorithm which finds an edge of the least possible weight that connects any two trees in the forest. This algorithm is a Greedy Algorithm. The steps to find a MST using this algorithm are as follows: Sort all the edges in non-decreasing order of their weight. Pick the smallest edge. Check if it forms a cycle with the spanning tree formed so far. If cycle is not formed, include this edge. Else, discard it. Repeat step2 until there are (V-1) edges in the spanning tree. The graph must have 10 vertices and 20 weighted edges.

You are given a weighted tree T.(As a reminder, a tree T is a graph that is connected and contains no cycle.) Each node of the tree T has a weight, denoted by w(v). You want to select a subset of tree nodes, such that weight of the selected nodes is maximized, and if a node is selected, then none of its neighbors are selected.

We have established a family tree and each node in the family tree is a member. Now we want to find out how many family members are in the family. Please write down the algorithm.

Operations Research (OR)