7 a) Use Dijkstra's algorithm to find the shortest path tree rooted at node B for the graph below. Label the vertices according to the algorithm. TI F 3 1 2 E B 6 8 1 3 1 9 5 D C b). Suppose the cost of every edge touching node B is increased by a non-negative constant. Are we guaranteed that the shortest path tree rooted at B remains the same? Explain.

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