Suppose that the edges of Kn are weighted-- what is the largest number of edges that cou be in the shortest path between two vertices in Kn? Your answer should be true for all n. O 2() O [n/2] O (3) On – 1
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- how can I prove that "if G has no isolated vertices and has a walk that uses all the edges, then G is connected."Indicate two edges such that after deleting these two edges the resulting graph is bipartite. Then to justify that the resulting graph is bipartite indicate the blue nodes and the red nodes.Find the shortest path from vertex ‘a’ to ‘z’ by Dijkstra’s algorithm for the weighted graph
- [PART IV] Find the shortest path from a to z. Using Trial and Error using Dijkstra’s algorithm.Consider the 8-city traveling salesman problem whose links have the associated distances shown in the following table (where a dash indicates the absence of a link). City 1 is the home city. Using 1-2-3-4-5-6-7-8-1 as the initial trial solution, perform three iterations of simulated annealing algorithm.Within a group of 12 women, there are five who have known each other for a long time and have an excellent relationship. The other 7 women do not know the 5 friends nor do they know each other. Whenever a subset of the five friends is equal to or greater than 50% of the number of people in another work group (for example, if there are two of the five friends in the work group of three or four people), then the group work becomes high performance It is desired to form a working group by selecting five women from the 12 women. What is the probability that the work group is high performing? Please indicate your answer in the space provided below as a number between zero and one, to four decimal places.
- Consider graphs with 9 vertices. What is the maximum number of edges in the graphs with Eulerian trails?Does the bipartite graph of K4, has a Hamilton path or is it Hamiltonian? Explain why it is a Hamilton path or Hamiltonian.Prove that a simple 2-connected graph G with at least four vertices is 3-connected if and only if for every triple (x, y, z) of distinct vertices and any edge e not incident with y, G has an x, z-path through e that does not contain y.
- Explain the step by step procedure of Dijktra’s algorithm to find the shortest path between any two vertices?The following table presents the implementation of Dijkstra's algorithm on the evaluated graph G with 8 vertices. How many different shortest paths exist in the graph G between the vertices a and g?A Hamiltonian path in a network is a closed path thatpasses exactly once through each node in the network before returning to its starting point. Taking a four-city TSP as anexample, explain why solving a TSP is equivalent to findingthe shortest Hamiltonian path in a network.