To list the vertices in each connected component after each iteration of CONNECTED-COMPONENETS procedure.

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Chapter 21.1, Problem 1E

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To list the vertices in each connected component after each iteration of CONNECTED-COMPONENETS procedure.

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2. Let G = (V, E) be a directed weighted graph with the vertices V = {A, B, C, D, E, F) and the edges E= {(A, B, 12), (A, D, 17), (B, C, 8), (B, D, 13), (B, E, 15), (B, F, 13), (C, E, 12), (C, F, 25)}, where the third components is the cost. (a) Write down the adjacency list representation the graph G = (V, E).

How do I do this? We say a graph G = (V, E) has a k-coloring for some positive integer k if we can assign k different colors to vertices of G such that for every edge (v, w) ∈ E, the color of v is different to the color w. More formally, G = (V, E) has a k-coloring if there is a function f : V → {1, 2, . . . , k} such that for every (v, w) ∈ E, f(v) 6= f(w).3-Color problem is defined as follows: Given a graph G = (V, E), does it have a 3-coloring?4-Color problem is defined as follows: Given a graph G = (V, E), does it have a 4-coloring?Prove that 3-Color ≤P 4-Color.(hint: add vertex to 3-Color problem instance.)

We are given an undirected connected graph G = (V, E) and vertices s and t.Initially, there is a robot at position s and we want to move this robot to position t by moving it along theedges of the graph; at any time step, we can move the robot to one of the neighboring vertices and the robotwill reach that vertex in the next time step.However, we have a problem: at every time step, a subset of vertices of this graph undergo maintenance andif the robot is on one of these vertices at this time step, it will be destroyed (!). Luckily, we are given theschedule of the maintenance for the next T time steps in an array M [1 : T ], where each M [i] is a linked-listof the vertices that undergo maintenance at time step i.Design an algorithm that finds a route for the robot to go from s to t in at most T seconds so that at notime i, the robot is on one of the maintained vertices, or output that this is not possible. The runtime ofyour algorithm should ideally be O((n + m) ·T ) but you will…