suppose that a graph G has MST already computed. How quickly can we update the MST if we add a new vertex and incident edges to it. I know for the best case scenario when a single edge is incident from the newly added vertex. but for the worst case, when ... many edges. This will end up being linear time since we can reuse part of the DFS that we had already computed before detecting each cycle.

Consider the following graph and Assume node ‘P’ as the starting vertex for Prim’s algorithm. Which of the following can be the correct order of edges in which they are added to construct Minimum Spanning Tree (MST)? P-Q, P-X, X-V, V-U, U-R, R-S, R-W, S-T P-Q, P-X, X-V, V-U, U-R, R-W, R-S, S-T P-Q, Q-R, R-W, W-V, V-X, V-U, R-S, S-T P-Q, Q-R, R-W, R-S, V-X, V-U, W-V, S-T

Here the graph that I was trying to find MST using algo in cormen.(If you need algo to ask, I supposed you have it) Algorithms uses min queue in process, my dobut is when it came to choice b/w vertex 'c' and 'd' as at that time both will have 8 has key ... we get wrong answer, so prism deal with this case? If you need algo I will given you, or just please refer chapter 23 cormen prim's algorithm.