Consider Dijkstra's link$-$state routing algorithm that is computing a least$-$cost path from node a to other nodes b$,$ c$,$ d$,$ e$,$ f$.$ Which of the following statements is true. $($choose all that apply$)$

In the initialization step, the initial cost from a to each of these destinations is initialized to cither the cost of a link directly connecting a to a direct neighbor, or infinity otherwise.

Suppose nodes b$,$ c$,$ and d are in the set N: These nodes will remain in $N^{\text{'}}$ for the rest of the algorithm, since the least$-$cost paths from a to b$,$ c$,$ and d are known.,

The values computed in the vector $D(v),$ the currently known least cost of a path from a to any node $v,$ will never increase following an iteration.

Following the initialization step, if nodes $b$ and $c$ are directly connected to $a,$ then the least cost path to $b$ and $c$ will never change from this initial cost.

The values computed in the vector $D(v),$ the currently known least cost of a path from a to any node $v,$ will always decrease following an iteration.