To get a lower bound of nlogn I am taking the sorting algorithm, which is well known to have that, and transforming/adapting it to Dijkstra's single source shortest path problem.I know you need to do create a graph based on the numeric values and that Dijkstra will traverse it in order, any help with the rest and how to evaluate it?Thank you.
Transforming the sorting problem into Dijkstra
shortest path
What you want is to reduce sorting (or element uniqueness) to the single source shortest path problem (rather than to Dijkstra's particular algorithm!) using an $o(n\log n)$ time reduction whose output has size $O(n)$. Then you will get a tight decision tree lower bound in the algebraic decision tree model for constant degree (Dijkstra's algorithm can be implemented using a linear algebraic decision tree).Such a reduction is probably not known. See for example D.W.'s question on cstheory.