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Let G=(V,E) be a graph for which all nodes have degree 5 and where G is 5-edge is connected.
a) Show that the vector x which is indexed by the edges E and for which xe = 1/5 for all e in E is in the Perfect Matching Polytope PPM.
b) Use your result in a) to show that G must have a perfect matching.
c) Show that b) may not be true if G is only 1-edge connected (but still has degree 5 everywhere) by giving an example of such a graph G which has no perfect matching.
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Q. Illustrate the result of running BFS and DFS on the directed graph given below using vertex 3 as source. Show the status of the data structure used at each and every stage.
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I need a person who has a good background in using R. Studio? In adition, a person who is good in using algorithms.
Example: (Double left rotation while a new node is added into the AVL tree (RL rotation)) Figure: Double left rotation when a new node is inserted into the AVL tree A
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