The edge weights of only those edges that are in the MST are given in graph G (screenshot). What is the minimum possible summation of edge weights for the edges (a, b), (e, d), (c, d)?. As you justify your answer for edge weights, please use graph G and apply Kruskal’s algorithm to obtain the MST step by step. Show and explain all your work.

Consider the following descriptions for one sample of six zones: Z1 matches B or D; Z2 matches C, E, or F; Z3 matches A or F; Z4 matches B or D; Z5 matches C or F; and Z6 matches D. (a) (A-F). Draw the bipartite graph that models the zones (Z1-Z6) and the letters they match (b) district layout. Use Hall's theorem to determine if algorithm will be able to successfully create a

Create a Python implementation of the provided image using the criteria below:Iteratively removes the edge with the highest weight from T until the specified number of 4 clusters is obtained after first creating the MST T of the provided weighted graph in Figure. It should be noted that this algorithm can be easily modified to evaluate edge weights of T that are greater than.

Consider this graph with 11 vertices and 20 edges. Our goal is to colour each of the 11 vertices with one of three colours (Apricot, Brown, Cyan) so that no edge joins two vertices of the same colour. For example, if the vertex 6 is coloured Brown, then the four vertices adjacent to this vertex (10, 5, 2, 7) cannot be coloured Brown, since that would create a Brown-Brown edge. If we can assign a colour to each vertex so that no edge joins two vertices of the same colour, then we say that this graph is 3-Colourable. If this task is impossible (i.e., no matter what, we must create at least one edge joining two vertices of the same colour), then we say that this graph is not 3-Colourable. Determine whether this graph is 3-Colourable. Answer either YES or NO.